Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [966,2,Mod(277,966)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(966, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("966.277");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 966.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.71354883526\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 13x^{6} + 10x^{5} + 47x^{4} + 180x^{3} + 220x^{2} + 768x + 1164 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 277.2 | ||
Root | \(1.26426 - 2.63252i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 966.277 |
Dual form | 966.2.i.m.415.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/966\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(829\) | \(925\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | −1.26426 | − | 2.18976i | −0.565394 | − | 0.979292i | −0.997013 | − | 0.0772356i | \(-0.975391\pi\) |
0.431618 | − | 0.902056i | \(-0.357943\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −2.41196 | − | 1.08740i | −0.911635 | − | 0.411000i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | −1.26426 | + | 2.18976i | −0.399794 | + | 0.692464i | ||||
\(11\) | −2.14770 | + | 3.71993i | −0.647556 | + | 1.12160i | 0.336149 | + | 0.941809i | \(0.390875\pi\) |
−0.983705 | + | 0.179791i | \(0.942458\pi\) | |||||||
\(12\) | 0.500000 | + | 0.866025i | 0.144338 | + | 0.250000i | ||||
\(13\) | 0.393417 | 0.109114 | 0.0545571 | − | 0.998511i | \(-0.482625\pi\) | ||||
0.0545571 | + | 0.998511i | \(0.482625\pi\) | |||||||
\(14\) | 0.264260 | + | 2.63252i | 0.0706265 | + | 0.703571i | ||||
\(15\) | −2.52852 | −0.652861 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −3.41196 | + | 5.90969i | −0.827522 | + | 1.43331i | 0.0724547 | + | 0.997372i | \(0.476917\pi\) |
−0.899977 | + | 0.435938i | \(0.856417\pi\) | |||||||
\(18\) | −0.500000 | + | 0.866025i | −0.117851 | + | 0.204124i | ||||
\(19\) | 1.00000 | + | 1.73205i | 0.229416 | + | 0.397360i | 0.957635 | − | 0.287984i | \(-0.0929851\pi\) |
−0.728219 | + | 0.685344i | \(0.759652\pi\) | |||||||
\(20\) | 2.52852 | 0.565394 | ||||||||
\(21\) | −2.14770 | + | 1.54512i | −0.468667 | + | 0.337172i | ||||
\(22\) | 4.29540 | 0.915782 | ||||||||
\(23\) | 0.500000 | + | 0.866025i | 0.104257 | + | 0.180579i | ||||
\(24\) | 0.500000 | − | 0.866025i | 0.102062 | − | 0.176777i | ||||
\(25\) | −0.696708 | + | 1.20673i | −0.139342 | + | 0.241347i | ||||
\(26\) | −0.196708 | − | 0.340709i | −0.0385777 | − | 0.0668185i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 2.14770 | − | 1.54512i | 0.405877 | − | 0.292000i | ||||
\(29\) | 4.60658 | 0.855421 | 0.427711 | − | 0.903916i | \(-0.359320\pi\) | ||||
0.427711 | + | 0.903916i | \(0.359320\pi\) | |||||||
\(30\) | 1.26426 | + | 2.18976i | 0.230821 | + | 0.399794i | ||||
\(31\) | 1.00000 | − | 1.73205i | 0.179605 | − | 0.311086i | −0.762140 | − | 0.647412i | \(-0.775851\pi\) |
0.941745 | + | 0.336327i | \(0.109185\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 2.14770 | + | 3.71993i | 0.373867 | + | 0.647556i | ||||
\(34\) | 6.82392 | 1.17029 | ||||||||
\(35\) | 0.668188 | + | 6.65638i | 0.112944 | + | 1.12513i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −4.52852 | − | 7.84363i | −0.744484 | − | 1.28948i | −0.950435 | − | 0.310922i | \(-0.899362\pi\) |
0.205951 | − | 0.978562i | \(-0.433971\pi\) | |||||||
\(38\) | 1.00000 | − | 1.73205i | 0.162221 | − | 0.280976i | ||||
\(39\) | 0.196708 | − | 0.340709i | 0.0314986 | − | 0.0545571i | ||||
\(40\) | −1.26426 | − | 2.18976i | −0.199897 | − | 0.346232i | ||||
\(41\) | −3.05704 | −0.477430 | −0.238715 | − | 0.971090i | \(-0.576726\pi\) | ||||
−0.238715 | + | 0.971090i | \(0.576726\pi\) | |||||||
\(42\) | 2.41196 | + | 1.08740i | 0.372174 | + | 0.167790i | ||||
\(43\) | 2.00000 | 0.304997 | 0.152499 | − | 0.988304i | \(-0.451268\pi\) | ||||
0.152499 | + | 0.988304i | \(0.451268\pi\) | |||||||
\(44\) | −2.14770 | − | 3.71993i | −0.323778 | − | 0.560800i | ||||
\(45\) | −1.26426 | + | 2.18976i | −0.188465 | + | 0.326431i | ||||
\(46\) | 0.500000 | − | 0.866025i | 0.0737210 | − | 0.127688i | ||||
\(47\) | 4.79540 | + | 8.30588i | 0.699481 | + | 1.21154i | 0.968647 | + | 0.248443i | \(0.0799187\pi\) |
−0.269166 | + | 0.963094i | \(0.586748\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 4.63510 | + | 5.24555i | 0.662158 | + | 0.749365i | ||||
\(50\) | 1.39342 | 0.197059 | ||||||||
\(51\) | 3.41196 | + | 5.90969i | 0.477770 | + | 0.827522i | ||||
\(52\) | −0.196708 | + | 0.340709i | −0.0272786 | + | 0.0472478i | ||||
\(53\) | −0.129157 | + | 0.223706i | −0.0177410 | + | 0.0307283i | −0.874760 | − | 0.484557i | \(-0.838981\pi\) |
0.857019 | + | 0.515285i | \(0.172314\pi\) | |||||||
\(54\) | 0.500000 | + | 0.866025i | 0.0680414 | + | 0.117851i | ||||
\(55\) | 10.8610 | 1.46450 | ||||||||
\(56\) | −2.41196 | − | 1.08740i | −0.322312 | − | 0.145311i | ||||
\(57\) | 2.00000 | 0.264906 | ||||||||
\(58\) | −2.30329 | − | 3.98942i | −0.302437 | − | 0.523836i | ||||
\(59\) | −5.05704 | + | 8.75905i | −0.658371 | + | 1.14033i | 0.322667 | + | 0.946513i | \(0.395421\pi\) |
−0.981037 | + | 0.193819i | \(0.937913\pi\) | |||||||
\(60\) | 1.26426 | − | 2.18976i | 0.163215 | − | 0.282697i | ||||
\(61\) | −1.60658 | − | 2.78268i | −0.205702 | − | 0.356286i | 0.744654 | − | 0.667450i | \(-0.232614\pi\) |
−0.950356 | + | 0.311164i | \(0.899281\pi\) | |||||||
\(62\) | −2.00000 | −0.254000 | ||||||||
\(63\) | 0.264260 | + | 2.63252i | 0.0332937 | + | 0.331666i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.497381 | − | 0.861490i | −0.0616926 | − | 0.106855i | ||||
\(66\) | 2.14770 | − | 3.71993i | 0.264364 | − | 0.457891i | ||||
\(67\) | −1.87084 | + | 3.24040i | −0.228560 | + | 0.395877i | −0.957382 | − | 0.288826i | \(-0.906735\pi\) |
0.728822 | + | 0.684704i | \(0.240068\pi\) | |||||||
\(68\) | −3.41196 | − | 5.90969i | −0.413761 | − | 0.716655i | ||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 5.43050 | − | 3.90686i | 0.649069 | − | 0.466959i | ||||
\(71\) | −13.8610 | −1.64500 | −0.822499 | − | 0.568766i | \(-0.807421\pi\) | ||||
−0.822499 | + | 0.568766i | \(0.807421\pi\) | |||||||
\(72\) | −0.500000 | − | 0.866025i | −0.0589256 | − | 0.102062i | ||||
\(73\) | −2.10658 | + | 3.64871i | −0.246557 | + | 0.427049i | −0.962568 | − | 0.271040i | \(-0.912633\pi\) |
0.716011 | + | 0.698089i | \(0.245966\pi\) | |||||||
\(74\) | −4.52852 | + | 7.84363i | −0.526430 | + | 0.911803i | ||||
\(75\) | 0.696708 | + | 1.20673i | 0.0804490 | + | 0.139342i | ||||
\(76\) | −2.00000 | −0.229416 | ||||||||
\(77\) | 9.22523 | − | 6.63689i | 1.05131 | − | 0.756344i | ||||
\(78\) | −0.393417 | −0.0445457 | ||||||||
\(79\) | −1.85230 | − | 3.20828i | −0.208400 | − | 0.360959i | 0.742811 | − | 0.669502i | \(-0.233492\pi\) |
−0.951211 | + | 0.308542i | \(0.900159\pi\) | |||||||
\(80\) | −1.26426 | + | 2.18976i | −0.141349 | + | 0.244823i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 1.52852 | + | 2.64748i | 0.168797 | + | 0.292365i | ||||
\(83\) | −13.6478 | −1.49805 | −0.749023 | − | 0.662544i | \(-0.769477\pi\) | ||||
−0.749023 | + | 0.662544i | \(0.769477\pi\) | |||||||
\(84\) | −0.264260 | − | 2.63252i | −0.0288332 | − | 0.287232i | ||||
\(85\) | 17.2544 | 1.87151 | ||||||||
\(86\) | −1.00000 | − | 1.73205i | −0.107833 | − | 0.186772i | ||||
\(87\) | 2.30329 | − | 3.98942i | 0.246939 | − | 0.427711i | ||||
\(88\) | −2.14770 | + | 3.71993i | −0.228946 | + | 0.396545i | ||||
\(89\) | 4.13510 | + | 7.16221i | 0.438320 | + | 0.759193i | 0.997560 | − | 0.0698131i | \(-0.0222403\pi\) |
−0.559240 | + | 0.829006i | \(0.688907\pi\) | |||||||
\(90\) | 2.52852 | 0.266529 | ||||||||
\(91\) | −0.948906 | − | 0.427803i | −0.0994724 | − | 0.0448460i | ||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | −1.00000 | − | 1.73205i | −0.103695 | − | 0.179605i | ||||
\(94\) | 4.79540 | − | 8.30588i | 0.494608 | − | 0.856686i | ||||
\(95\) | 2.52852 | − | 4.37953i | 0.259421 | − | 0.449330i | ||||
\(96\) | 0.500000 | + | 0.866025i | 0.0510310 | + | 0.0883883i | ||||
\(97\) | −8.00000 | −0.812277 | −0.406138 | − | 0.913812i | \(-0.633125\pi\) | ||||
−0.406138 | + | 0.913812i | \(0.633125\pi\) | |||||||
\(98\) | 2.22523 | − | 6.63689i | 0.224782 | − | 0.670427i | ||||
\(99\) | 4.29540 | 0.431704 | ||||||||
\(100\) | −0.696708 | − | 1.20673i | −0.0696708 | − | 0.120673i | ||||
\(101\) | −2.69671 | + | 4.67084i | −0.268333 | + | 0.464766i | −0.968431 | − | 0.249280i | \(-0.919806\pi\) |
0.700099 | + | 0.714046i | \(0.253139\pi\) | |||||||
\(102\) | 3.41196 | − | 5.90969i | 0.337834 | − | 0.585146i | ||||
\(103\) | 9.07558 | + | 15.7194i | 0.894244 | + | 1.54888i | 0.834738 | + | 0.550648i | \(0.185619\pi\) |
0.0595064 | + | 0.998228i | \(0.481047\pi\) | |||||||
\(104\) | 0.393417 | 0.0385777 | ||||||||
\(105\) | 6.09869 | + | 2.74952i | 0.595171 | + | 0.268326i | ||||
\(106\) | 0.258313 | 0.0250896 | ||||||||
\(107\) | −8.29540 | − | 14.3681i | −0.801947 | − | 1.38901i | −0.918333 | − | 0.395808i | \(-0.870465\pi\) |
0.116387 | − | 0.993204i | \(-0.462869\pi\) | |||||||
\(108\) | 0.500000 | − | 0.866025i | 0.0481125 | − | 0.0833333i | ||||
\(109\) | −7.28280 | + | 12.6142i | −0.697566 | + | 1.20822i | 0.271742 | + | 0.962370i | \(0.412400\pi\) |
−0.969308 | + | 0.245850i | \(0.920933\pi\) | |||||||
\(110\) | −5.43050 | − | 9.40591i | −0.517778 | − | 0.896818i | ||||
\(111\) | −9.05704 | −0.859656 | ||||||||
\(112\) | 0.264260 | + | 2.63252i | 0.0249703 | + | 0.248750i | ||||
\(113\) | −9.11932 | −0.857873 | −0.428937 | − | 0.903335i | \(-0.641112\pi\) | ||||
−0.428937 | + | 0.903335i | \(0.641112\pi\) | |||||||
\(114\) | −1.00000 | − | 1.73205i | −0.0936586 | − | 0.162221i | ||||
\(115\) | 1.26426 | − | 2.18976i | 0.117893 | − | 0.204196i | ||||
\(116\) | −2.30329 | + | 3.98942i | −0.213855 | + | 0.370408i | ||||
\(117\) | −0.196708 | − | 0.340709i | −0.0181857 | − | 0.0314986i | ||||
\(118\) | 10.1141 | 0.931077 | ||||||||
\(119\) | 14.6557 | − | 10.5438i | 1.34349 | − | 0.966544i | ||||
\(120\) | −2.52852 | −0.230821 | ||||||||
\(121\) | −3.72523 | − | 6.45229i | −0.338657 | − | 0.586571i | ||||
\(122\) | −1.60658 | + | 2.78268i | −0.145453 | + | 0.251932i | ||||
\(123\) | −1.52852 | + | 2.64748i | −0.137822 | + | 0.238715i | ||||
\(124\) | 1.00000 | + | 1.73205i | 0.0898027 | + | 0.155543i | ||||
\(125\) | −9.11932 | −0.815657 | ||||||||
\(126\) | 2.14770 | − | 1.54512i | 0.191332 | − | 0.137650i | ||||
\(127\) | 6.27021 | 0.556391 | 0.278195 | − | 0.960524i | \(-0.410264\pi\) | ||||
0.278195 | + | 0.960524i | \(0.410264\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 1.00000 | − | 1.73205i | 0.0880451 | − | 0.152499i | ||||
\(130\) | −0.497381 | + | 0.861490i | −0.0436232 | + | 0.0755577i | ||||
\(131\) | 9.54915 | + | 16.5396i | 0.834313 | + | 1.44507i | 0.894588 | + | 0.446891i | \(0.147469\pi\) |
−0.0602754 | + | 0.998182i | \(0.519198\pi\) | |||||||
\(132\) | −4.29540 | −0.373867 | ||||||||
\(133\) | −0.528521 | − | 5.26504i | −0.0458286 | − | 0.456537i | ||||
\(134\) | 3.74169 | 0.323233 | ||||||||
\(135\) | 1.26426 | + | 2.18976i | 0.108810 | + | 0.188465i | ||||
\(136\) | −3.41196 | + | 5.90969i | −0.292573 | + | 0.506752i | ||||
\(137\) | 8.76440 | − | 15.1804i | 0.748793 | − | 1.29695i | −0.199608 | − | 0.979876i | \(-0.563967\pi\) |
0.948401 | − | 0.317072i | \(-0.102700\pi\) | |||||||
\(138\) | −0.500000 | − | 0.866025i | −0.0425628 | − | 0.0737210i | ||||
\(139\) | 13.0413 | 1.10615 | 0.553073 | − | 0.833133i | \(-0.313455\pi\) | ||||
0.553073 | + | 0.833133i | \(0.313455\pi\) | |||||||
\(140\) | −6.09869 | − | 2.74952i | −0.515433 | − | 0.232377i | ||||
\(141\) | 9.59080 | 0.807691 | ||||||||
\(142\) | 6.93050 | + | 12.0040i | 0.581595 | + | 1.00735i | ||||
\(143\) | −0.844941 | + | 1.46348i | −0.0706575 | + | 0.122382i | ||||
\(144\) | −0.500000 | + | 0.866025i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | −5.82392 | − | 10.0873i | −0.483650 | − | 0.837707i | ||||
\(146\) | 4.21317 | 0.348684 | ||||||||
\(147\) | 6.86033 | − | 1.39134i | 0.565831 | − | 0.114756i | ||||
\(148\) | 9.05704 | 0.744484 | ||||||||
\(149\) | 0.0311393 | + | 0.0539349i | 0.00255103 | + | 0.00441852i | 0.867298 | − | 0.497789i | \(-0.165855\pi\) |
−0.864747 | + | 0.502208i | \(0.832521\pi\) | |||||||
\(150\) | 0.696708 | − | 1.20673i | 0.0568860 | − | 0.0985295i | ||||
\(151\) | 1.07806 | − | 1.86726i | 0.0877315 | − | 0.151955i | −0.818820 | − | 0.574050i | \(-0.805372\pi\) |
0.906552 | + | 0.422094i | \(0.138705\pi\) | |||||||
\(152\) | 1.00000 | + | 1.73205i | 0.0811107 | + | 0.140488i | ||||
\(153\) | 6.82392 | 0.551681 | ||||||||
\(154\) | −10.3603 | − | 4.67084i | −0.834859 | − | 0.376387i | ||||
\(155\) | −5.05704 | −0.406191 | ||||||||
\(156\) | 0.196708 | + | 0.340709i | 0.0157493 | + | 0.0272786i | ||||
\(157\) | −5.54112 | + | 9.59750i | −0.442229 | + | 0.765964i | −0.997855 | − | 0.0654693i | \(-0.979146\pi\) |
0.555625 | + | 0.831433i | \(0.312479\pi\) | |||||||
\(158\) | −1.85230 | + | 3.20828i | −0.147361 | + | 0.255237i | ||||
\(159\) | 0.129157 | + | 0.223706i | 0.0102428 | + | 0.0177410i | ||||
\(160\) | 2.52852 | 0.199897 | ||||||||
\(161\) | −0.264260 | − | 2.63252i | −0.0208266 | − | 0.207472i | ||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −6.12721 | − | 10.6126i | −0.479920 | − | 0.831246i | 0.519814 | − | 0.854279i | \(-0.326001\pi\) |
−0.999735 | + | 0.0230329i | \(0.992668\pi\) | |||||||
\(164\) | 1.52852 | − | 2.64748i | 0.119357 | − | 0.206733i | ||||
\(165\) | 5.43050 | − | 9.40591i | 0.422764 | − | 0.732249i | ||||
\(166\) | 6.82392 | + | 11.8194i | 0.529639 | + | 0.917362i | ||||
\(167\) | 4.81975 | 0.372963 | 0.186482 | − | 0.982458i | \(-0.440291\pi\) | ||||
0.186482 | + | 0.982458i | \(0.440291\pi\) | |||||||
\(168\) | −2.14770 | + | 1.54512i | −0.165699 | + | 0.119208i | ||||
\(169\) | −12.8452 | −0.988094 | ||||||||
\(170\) | −8.62721 | − | 14.9428i | −0.661677 | − | 1.14606i | ||||
\(171\) | 1.00000 | − | 1.73205i | 0.0764719 | − | 0.132453i | ||||
\(172\) | −1.00000 | + | 1.73205i | −0.0762493 | + | 0.132068i | ||||
\(173\) | −11.4797 | − | 19.8833i | −0.872782 | − | 1.51170i | −0.859107 | − | 0.511796i | \(-0.828980\pi\) |
−0.0136749 | − | 0.999906i | \(-0.504353\pi\) | |||||||
\(174\) | −4.60658 | −0.349224 | ||||||||
\(175\) | 2.99264 | − | 2.15299i | 0.226222 | − | 0.162751i | ||||
\(176\) | 4.29540 | 0.323778 | ||||||||
\(177\) | 5.05704 | + | 8.75905i | 0.380111 | + | 0.658371i | ||||
\(178\) | 4.13510 | − | 7.16221i | 0.309939 | − | 0.536830i | ||||
\(179\) | −10.9226 | + | 18.9185i | −0.816394 | + | 1.41404i | 0.0919281 | + | 0.995766i | \(0.470697\pi\) |
−0.908322 | + | 0.418271i | \(0.862636\pi\) | |||||||
\(180\) | −1.26426 | − | 2.18976i | −0.0942324 | − | 0.163215i | ||||
\(181\) | −22.0994 | −1.64263 | −0.821316 | − | 0.570473i | \(-0.806760\pi\) | ||||
−0.821316 | + | 0.570473i | \(0.806760\pi\) | |||||||
\(182\) | 0.103964 | + | 1.03568i | 0.00770636 | + | 0.0767696i | ||||
\(183\) | −3.21317 | −0.237524 | ||||||||
\(184\) | 0.500000 | + | 0.866025i | 0.0368605 | + | 0.0638442i | ||||
\(185\) | −11.4505 | + | 19.8328i | −0.841854 | + | 1.45813i | ||||
\(186\) | −1.00000 | + | 1.73205i | −0.0733236 | + | 0.127000i | ||||
\(187\) | −14.6557 | − | 25.3845i | −1.07173 | − | 1.85630i | ||||
\(188\) | −9.59080 | −0.699481 | ||||||||
\(189\) | 2.41196 | + | 1.08740i | 0.175444 | + | 0.0790970i | ||||
\(190\) | −5.05704 | −0.366876 | ||||||||
\(191\) | 4.13510 | + | 7.16221i | 0.299206 | + | 0.518239i | 0.975954 | − | 0.217975i | \(-0.0699450\pi\) |
−0.676749 | + | 0.736214i | \(0.736612\pi\) | |||||||
\(192\) | 0.500000 | − | 0.866025i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | 3.25375 | − | 5.63566i | 0.234210 | − | 0.405664i | −0.724833 | − | 0.688925i | \(-0.758083\pi\) |
0.959043 | + | 0.283261i | \(0.0914163\pi\) | |||||||
\(194\) | 4.00000 | + | 6.92820i | 0.287183 | + | 0.497416i | ||||
\(195\) | −0.994763 | −0.0712364 | ||||||||
\(196\) | −6.86033 | + | 1.39134i | −0.490024 | + | 0.0993816i | ||||
\(197\) | 8.18025 | 0.582819 | 0.291409 | − | 0.956598i | \(-0.405876\pi\) | ||||
0.291409 | + | 0.956598i | \(0.405876\pi\) | |||||||
\(198\) | −2.14770 | − | 3.71993i | −0.152630 | − | 0.264364i | ||||
\(199\) | 7.20474 | − | 12.4790i | 0.510731 | − | 0.884611i | −0.489192 | − | 0.872176i | \(-0.662708\pi\) |
0.999923 | − | 0.0124352i | \(-0.00395836\pi\) | |||||||
\(200\) | −0.696708 | + | 1.20673i | −0.0492647 | + | 0.0853290i | ||||
\(201\) | 1.87084 | + | 3.24040i | 0.131959 | + | 0.228560i | ||||
\(202\) | 5.39342 | 0.379479 | ||||||||
\(203\) | −11.1109 | − | 5.00922i | −0.779832 | − | 0.351578i | ||||
\(204\) | −6.82392 | −0.477770 | ||||||||
\(205\) | 3.86490 | + | 6.69420i | 0.269936 | + | 0.467543i | ||||
\(206\) | 9.07558 | − | 15.7194i | 0.632326 | − | 1.09522i | ||||
\(207\) | 0.500000 | − | 0.866025i | 0.0347524 | − | 0.0601929i | ||||
\(208\) | −0.196708 | − | 0.340709i | −0.0136393 | − | 0.0236239i | ||||
\(209\) | −8.59080 | −0.594238 | ||||||||
\(210\) | −0.668188 | − | 6.65638i | −0.0461093 | − | 0.459334i | ||||
\(211\) | 15.1974 | 1.04623 | 0.523115 | − | 0.852262i | \(-0.324770\pi\) | ||||
0.523115 | + | 0.852262i | \(0.324770\pi\) | |||||||
\(212\) | −0.129157 | − | 0.223706i | −0.00887051 | − | 0.0153642i | ||||
\(213\) | −6.93050 | + | 12.0040i | −0.474870 | + | 0.822499i | ||||
\(214\) | −8.29540 | + | 14.3681i | −0.567062 | + | 0.982180i | ||||
\(215\) | −2.52852 | − | 4.37953i | −0.172444 | − | 0.298681i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −4.29540 | + | 3.09023i | −0.291591 | + | 0.209779i | ||||
\(218\) | 14.5656 | 0.986507 | ||||||||
\(219\) | 2.10658 | + | 3.64871i | 0.142350 | + | 0.246557i | ||||
\(220\) | −5.43050 | + | 9.40591i | −0.366124 | + | 0.634146i | ||||
\(221\) | −1.34232 | + | 2.32497i | −0.0902944 | + | 0.156394i | ||||
\(222\) | 4.52852 | + | 7.84363i | 0.303934 | + | 0.526430i | ||||
\(223\) | −21.1711 | −1.41772 | −0.708862 | − | 0.705348i | \(-0.750791\pi\) | ||||
−0.708862 | + | 0.705348i | \(0.750791\pi\) | |||||||
\(224\) | 2.14770 | − | 1.54512i | 0.143499 | − | 0.103237i | ||||
\(225\) | 1.39342 | 0.0928945 | ||||||||
\(226\) | 4.55966 | + | 7.89756i | 0.303304 | + | 0.525338i | ||||
\(227\) | 1.20474 | − | 2.08667i | 0.0799615 | − | 0.138497i | −0.823272 | − | 0.567648i | \(-0.807854\pi\) |
0.903233 | + | 0.429150i | \(0.141187\pi\) | |||||||
\(228\) | −1.00000 | + | 1.73205i | −0.0662266 | + | 0.114708i | ||||
\(229\) | −5.30800 | − | 9.19372i | −0.350762 | − | 0.607538i | 0.635621 | − | 0.772001i | \(-0.280744\pi\) |
−0.986383 | + | 0.164463i | \(0.947411\pi\) | |||||||
\(230\) | −2.52852 | −0.166726 | ||||||||
\(231\) | −1.13510 | − | 11.3077i | −0.0746843 | − | 0.743994i | ||||
\(232\) | 4.60658 | 0.302437 | ||||||||
\(233\) | −6.59080 | − | 11.4156i | −0.431778 | − | 0.747861i | 0.565249 | − | 0.824920i | \(-0.308780\pi\) |
−0.997026 | + | 0.0770597i | \(0.975447\pi\) | |||||||
\(234\) | −0.196708 | + | 0.340709i | −0.0128592 | + | 0.0222728i | ||||
\(235\) | 12.1253 | − | 21.0016i | 0.790965 | − | 1.36999i | ||||
\(236\) | −5.05704 | − | 8.75905i | −0.329185 | − | 0.570166i | ||||
\(237\) | −3.70460 | −0.240640 | ||||||||
\(238\) | −16.4590 | − | 7.42036i | −1.06688 | − | 0.480991i | ||||
\(239\) | 4.25442 | 0.275196 | 0.137598 | − | 0.990488i | \(-0.456062\pi\) | ||||
0.137598 | + | 0.990488i | \(0.456062\pi\) | |||||||
\(240\) | 1.26426 | + | 2.18976i | 0.0816077 | + | 0.141349i | ||||
\(241\) | −7.76688 | + | 13.4526i | −0.500309 | + | 0.866560i | 0.499691 | + | 0.866204i | \(0.333447\pi\) |
−1.00000 | 0.000356441i | \(0.999887\pi\) | ||||||||
\(242\) | −3.72523 | + | 6.45229i | −0.239467 | + | 0.414769i | ||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 3.21317 | 0.205702 | ||||||||
\(245\) | 5.62654 | − | 16.7815i | 0.359466 | − | 1.07213i | ||||
\(246\) | 3.05704 | 0.194910 | ||||||||
\(247\) | 0.393417 | + | 0.681418i | 0.0250325 | + | 0.0433576i | ||||
\(248\) | 1.00000 | − | 1.73205i | 0.0635001 | − | 0.109985i | ||||
\(249\) | −6.82392 | + | 11.8194i | −0.432448 | + | 0.749023i | ||||
\(250\) | 4.55966 | + | 7.89756i | 0.288378 | + | 0.499486i | ||||
\(251\) | −21.4266 | −1.35244 | −0.676218 | − | 0.736702i | \(-0.736382\pi\) | ||||
−0.676218 | + | 0.736702i | \(0.736382\pi\) | |||||||
\(252\) | −2.41196 | − | 1.08740i | −0.151939 | − | 0.0685000i | ||||
\(253\) | −4.29540 | −0.270049 | ||||||||
\(254\) | −3.13510 | − | 5.43016i | −0.196714 | − | 0.340718i | ||||
\(255\) | 8.62721 | − | 14.9428i | 0.540257 | − | 0.935753i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −9.76688 | − | 16.9167i | −0.609241 | − | 1.05524i | −0.991366 | − | 0.131126i | \(-0.958141\pi\) |
0.382125 | − | 0.924111i | \(-0.375193\pi\) | |||||||
\(258\) | −2.00000 | −0.124515 | ||||||||
\(259\) | 2.39342 | + | 23.8429i | 0.148720 | + | 1.48152i | ||||
\(260\) | 0.994763 | 0.0616926 | ||||||||
\(261\) | −2.30329 | − | 3.98942i | −0.142570 | − | 0.246939i | ||||
\(262\) | 9.54915 | − | 16.5396i | 0.589948 | − | 1.02182i | ||||
\(263\) | −8.90198 | + | 15.4187i | −0.548920 | + | 0.950757i | 0.449429 | + | 0.893316i | \(0.351627\pi\) |
−0.998349 | + | 0.0574409i | \(0.981706\pi\) | |||||||
\(264\) | 2.14770 | + | 3.71993i | 0.132182 | + | 0.228946i | ||||
\(265\) | 0.653150 | 0.0401227 | ||||||||
\(266\) | −4.29540 | + | 3.09023i | −0.263368 | + | 0.189474i | ||||
\(267\) | 8.27021 | 0.506128 | ||||||||
\(268\) | −1.87084 | − | 3.24040i | −0.114280 | − | 0.197939i | ||||
\(269\) | 9.81603 | − | 17.0019i | 0.598494 | − | 1.03662i | −0.394550 | − | 0.918875i | \(-0.629099\pi\) |
0.993044 | − | 0.117747i | \(-0.0375672\pi\) | |||||||
\(270\) | 1.26426 | − | 2.18976i | 0.0769404 | − | 0.133265i | ||||
\(271\) | −4.68882 | − | 8.12127i | −0.284825 | − | 0.493332i | 0.687741 | − | 0.725956i | \(-0.258602\pi\) |
−0.972567 | + | 0.232624i | \(0.925269\pi\) | |||||||
\(272\) | 6.82392 | 0.413761 | ||||||||
\(273\) | −0.844941 | + | 0.607875i | −0.0511382 | + | 0.0367903i | ||||
\(274\) | −17.5288 | −1.05895 | ||||||||
\(275\) | −2.99264 | − | 5.18341i | −0.180463 | − | 0.312571i | ||||
\(276\) | −0.500000 | + | 0.866025i | −0.0300965 | + | 0.0521286i | ||||
\(277\) | 5.96359 | − | 10.3292i | 0.358317 | − | 0.620624i | −0.629363 | − | 0.777112i | \(-0.716684\pi\) |
0.987680 | + | 0.156488i | \(0.0500173\pi\) | |||||||
\(278\) | −6.52063 | − | 11.2941i | −0.391081 | − | 0.677373i | ||||
\(279\) | −2.00000 | −0.119737 | ||||||||
\(280\) | 0.668188 | + | 6.65638i | 0.0399319 | + | 0.397795i | ||||
\(281\) | −10.6783 | −0.637012 | −0.318506 | − | 0.947921i | \(-0.603181\pi\) | ||||
−0.318506 | + | 0.947921i | \(0.603181\pi\) | |||||||
\(282\) | −4.79540 | − | 8.30588i | −0.285562 | − | 0.494608i | ||||
\(283\) | 5.61670 | − | 9.72841i | 0.333878 | − | 0.578294i | −0.649390 | − | 0.760455i | \(-0.724976\pi\) |
0.983269 | + | 0.182161i | \(0.0583092\pi\) | |||||||
\(284\) | 6.93050 | − | 12.0040i | 0.411250 | − | 0.712305i | ||||
\(285\) | −2.52852 | − | 4.37953i | −0.149777 | − | 0.259421i | ||||
\(286\) | 1.68988 | 0.0999249 | ||||||||
\(287\) | 7.37346 | + | 3.32424i | 0.435242 | + | 0.196224i | ||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −14.7829 | − | 25.6048i | −0.869585 | − | 1.50617i | ||||
\(290\) | −5.82392 | + | 10.0873i | −0.341992 | + | 0.592348i | ||||
\(291\) | −4.00000 | + | 6.92820i | −0.234484 | + | 0.406138i | ||||
\(292\) | −2.10658 | − | 3.64871i | −0.123278 | − | 0.213525i | ||||
\(293\) | 22.1764 | 1.29556 | 0.647778 | − | 0.761829i | \(-0.275698\pi\) | ||||
0.647778 | + | 0.761829i | \(0.275698\pi\) | |||||||
\(294\) | −4.63510 | − | 5.24555i | −0.270325 | − | 0.305927i | ||||
\(295\) | 25.5737 | 1.48896 | ||||||||
\(296\) | −4.52852 | − | 7.84363i | −0.263215 | − | 0.455902i | ||||
\(297\) | 2.14770 | − | 3.71993i | 0.124622 | − | 0.215852i | ||||
\(298\) | 0.0311393 | − | 0.0539349i | 0.00180385 | − | 0.00312436i | ||||
\(299\) | 0.196708 | + | 0.340709i | 0.0113759 | + | 0.0197037i | ||||
\(300\) | −1.39342 | −0.0804490 | ||||||||
\(301\) | −4.82392 | − | 2.17481i | −0.278046 | − | 0.125354i | ||||
\(302\) | −2.15612 | −0.124071 | ||||||||
\(303\) | 2.69671 | + | 4.67084i | 0.154922 | + | 0.268333i | ||||
\(304\) | 1.00000 | − | 1.73205i | 0.0573539 | − | 0.0993399i | ||||
\(305\) | −4.06228 | + | 7.03607i | −0.232605 | + | 0.402884i | ||||
\(306\) | −3.41196 | − | 5.90969i | −0.195049 | − | 0.337834i | ||||
\(307\) | −8.01578 | −0.457485 | −0.228742 | − | 0.973487i | \(-0.573461\pi\) | ||||
−0.228742 | + | 0.973487i | \(0.573461\pi\) | |||||||
\(308\) | 1.13510 | + | 11.3077i | 0.0646785 | + | 0.644318i | ||||
\(309\) | 18.1512 | 1.03258 | ||||||||
\(310\) | 2.52852 | + | 4.37953i | 0.143610 | + | 0.248740i | ||||
\(311\) | −10.7954 | + | 18.6982i | −0.612151 | + | 1.06028i | 0.378726 | + | 0.925509i | \(0.376362\pi\) |
−0.990877 | + | 0.134768i | \(0.956971\pi\) | |||||||
\(312\) | 0.196708 | − | 0.340709i | 0.0111364 | − | 0.0192889i | ||||
\(313\) | −6.59080 | − | 11.4156i | −0.372534 | − | 0.645248i | 0.617421 | − | 0.786633i | \(-0.288178\pi\) |
−0.989955 | + | 0.141385i | \(0.954844\pi\) | |||||||
\(314\) | 11.0822 | 0.625407 | ||||||||
\(315\) | 5.43050 | − | 3.90686i | 0.305974 | − | 0.220127i | ||||
\(316\) | 3.70460 | 0.208400 | ||||||||
\(317\) | 7.11408 | + | 12.3220i | 0.399567 | + | 0.692070i | 0.993672 | − | 0.112317i | \(-0.0358273\pi\) |
−0.594106 | + | 0.804387i | \(0.702494\pi\) | |||||||
\(318\) | 0.129157 | − | 0.223706i | 0.00724274 | − | 0.0125448i | ||||
\(319\) | −9.89356 | + | 17.1361i | −0.553933 | + | 0.959440i | ||||
\(320\) | −1.26426 | − | 2.18976i | −0.0706743 | − | 0.122411i | ||||
\(321\) | −16.5908 | −0.926008 | ||||||||
\(322\) | −2.14770 | + | 1.54512i | −0.119687 | + | 0.0861060i | ||||
\(323\) | −13.6478 | −0.759386 | ||||||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | −0.274097 | + | 0.474750i | −0.0152042 | + | 0.0263344i | ||||
\(326\) | −6.12721 | + | 10.6126i | −0.339355 | + | 0.587780i | ||||
\(327\) | 7.28280 | + | 12.6142i | 0.402740 | + | 0.697566i | ||||
\(328\) | −3.05704 | −0.168797 | ||||||||
\(329\) | −2.53447 | − | 25.2480i | −0.139730 | − | 1.39197i | ||||
\(330\) | −10.8610 | −0.597879 | ||||||||
\(331\) | 10.7987 | + | 18.7039i | 0.593552 | + | 1.02806i | 0.993749 | + | 0.111633i | \(0.0356081\pi\) |
−0.400198 | + | 0.916429i | \(0.631059\pi\) | |||||||
\(332\) | 6.82392 | − | 11.8194i | 0.374511 | − | 0.648673i | ||||
\(333\) | −4.52852 | + | 7.84363i | −0.248161 | + | 0.429828i | ||||
\(334\) | −2.40987 | − | 4.17403i | −0.131862 | − | 0.228393i | ||||
\(335\) | 9.46093 | 0.516906 | ||||||||
\(336\) | 2.41196 | + | 1.08740i | 0.131583 | + | 0.0593228i | ||||
\(337\) | 13.2132 | 0.719767 | 0.359884 | − | 0.932997i | \(-0.382816\pi\) | ||||
0.359884 | + | 0.932997i | \(0.382816\pi\) | |||||||
\(338\) | 6.42261 | + | 11.1243i | 0.349344 | + | 0.605082i | ||||
\(339\) | −4.55966 | + | 7.89756i | −0.247647 | + | 0.428937i | ||||
\(340\) | −8.62721 | + | 14.9428i | −0.467876 | + | 0.810385i | ||||
\(341\) | 4.29540 | + | 7.43985i | 0.232609 | + | 0.402890i | ||||
\(342\) | −2.00000 | −0.108148 | ||||||||
\(343\) | −5.47565 | − | 17.6923i | −0.295657 | − | 0.955294i | ||||
\(344\) | 2.00000 | 0.107833 | ||||||||
\(345\) | −1.26426 | − | 2.18976i | −0.0680655 | − | 0.117893i | ||||
\(346\) | −11.4797 | + | 19.8833i | −0.617150 | + | 1.06894i | ||||
\(347\) | 9.70945 | − | 16.8173i | 0.521230 | − | 0.902797i | −0.478465 | − | 0.878107i | \(-0.658807\pi\) |
0.999695 | − | 0.0246907i | \(-0.00786009\pi\) | |||||||
\(348\) | 2.30329 | + | 3.98942i | 0.123469 | + | 0.213855i | ||||
\(349\) | −5.80262 | −0.310607 | −0.155303 | − | 0.987867i | \(-0.549636\pi\) | ||||
−0.155303 | + | 0.987867i | \(0.549636\pi\) | |||||||
\(350\) | −3.36087 | − | 1.51521i | −0.179646 | − | 0.0809912i | ||||
\(351\) | −0.393417 | −0.0209990 | ||||||||
\(352\) | −2.14770 | − | 3.71993i | −0.114473 | − | 0.198273i | ||||
\(353\) | −10.4715 | + | 18.1371i | −0.557341 | + | 0.965342i | 0.440377 | + | 0.897813i | \(0.354845\pi\) |
−0.997717 | + | 0.0675291i | \(0.978488\pi\) | |||||||
\(354\) | 5.05704 | − | 8.75905i | 0.268779 | − | 0.465538i | ||||
\(355\) | 17.5239 | + | 30.3523i | 0.930073 | + | 1.61093i | ||||
\(356\) | −8.27021 | −0.438320 | ||||||||
\(357\) | −1.80329 | − | 17.9641i | −0.0954403 | − | 0.950762i | ||||
\(358\) | 21.8452 | 1.15456 | ||||||||
\(359\) | 2.35244 | + | 4.07455i | 0.124157 | + | 0.215046i | 0.921403 | − | 0.388608i | \(-0.127044\pi\) |
−0.797246 | + | 0.603654i | \(0.793711\pi\) | |||||||
\(360\) | −1.26426 | + | 2.18976i | −0.0666324 | + | 0.115411i | ||||
\(361\) | 7.50000 | − | 12.9904i | 0.394737 | − | 0.683704i | ||||
\(362\) | 11.0497 | + | 19.1386i | 0.580758 | + | 1.00590i | ||||
\(363\) | −7.45046 | −0.391048 | ||||||||
\(364\) | 0.844941 | − | 0.607875i | 0.0442870 | − | 0.0318613i | ||||
\(365\) | 10.6531 | 0.557608 | ||||||||
\(366\) | 1.60658 | + | 2.78268i | 0.0839774 | + | 0.145453i | ||||
\(367\) | 4.71996 | − | 8.17520i | 0.246380 | − | 0.426742i | −0.716139 | − | 0.697958i | \(-0.754092\pi\) |
0.962519 | + | 0.271216i | \(0.0874256\pi\) | |||||||
\(368\) | 0.500000 | − | 0.866025i | 0.0260643 | − | 0.0451447i | ||||
\(369\) | 1.52852 | + | 2.64748i | 0.0795716 | + | 0.137822i | ||||
\(370\) | 22.9009 | 1.19056 | ||||||||
\(371\) | 0.554779 | − | 0.399124i | 0.0288027 | − | 0.0207215i | ||||
\(372\) | 2.00000 | 0.103695 | ||||||||
\(373\) | −5.83652 | − | 10.1091i | −0.302203 | − | 0.523432i | 0.674431 | − | 0.738338i | \(-0.264389\pi\) |
−0.976635 | + | 0.214906i | \(0.931056\pi\) | |||||||
\(374\) | −14.6557 | + | 25.3845i | −0.757830 | + | 1.31260i | ||||
\(375\) | −4.55966 | + | 7.89756i | −0.235460 | + | 0.407828i | ||||
\(376\) | 4.79540 | + | 8.30588i | 0.247304 | + | 0.428343i | ||||
\(377\) | 1.81231 | 0.0933386 | ||||||||
\(378\) | −0.264260 | − | 2.63252i | −0.0135921 | − | 0.135402i | ||||
\(379\) | 9.42944 | 0.484358 | 0.242179 | − | 0.970232i | \(-0.422138\pi\) | ||||
0.242179 | + | 0.970232i | \(0.422138\pi\) | |||||||
\(380\) | 2.52852 | + | 4.37953i | 0.129710 | + | 0.224665i | ||||
\(381\) | 3.13510 | − | 5.43016i | 0.160616 | − | 0.278195i | ||||
\(382\) | 4.13510 | − | 7.16221i | 0.211570 | − | 0.366451i | ||||
\(383\) | 11.7049 | + | 20.2735i | 0.598092 | + | 1.03592i | 0.993103 | + | 0.117249i | \(0.0374074\pi\) |
−0.395011 | + | 0.918676i | \(0.629259\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −26.1963 | − | 11.8103i | −1.33509 | − | 0.601909i | ||||
\(386\) | −6.50750 | −0.331223 | ||||||||
\(387\) | −1.00000 | − | 1.73205i | −0.0508329 | − | 0.0880451i | ||||
\(388\) | 4.00000 | − | 6.92820i | 0.203069 | − | 0.351726i | ||||
\(389\) | 11.0371 | − | 19.1168i | 0.559603 | − | 0.969260i | −0.437927 | − | 0.899011i | \(-0.644287\pi\) |
0.997529 | − | 0.0702494i | \(-0.0223795\pi\) | |||||||
\(390\) | 0.497381 | + | 0.861490i | 0.0251859 | + | 0.0436232i | ||||
\(391\) | −6.82392 | −0.345100 | ||||||||
\(392\) | 4.63510 | + | 5.24555i | 0.234108 | + | 0.264940i | ||||
\(393\) | 19.0983 | 0.963382 | ||||||||
\(394\) | −4.09013 | − | 7.08430i | −0.206058 | − | 0.356902i | ||||
\(395\) | −4.68358 | + | 8.11220i | −0.235656 | + | 0.408169i | ||||
\(396\) | −2.14770 | + | 3.71993i | −0.107926 | + | 0.186933i | ||||
\(397\) | 8.41405 | + | 14.5736i | 0.422289 | + | 0.731426i | 0.996163 | − | 0.0875178i | \(-0.0278935\pi\) |
−0.573874 | + | 0.818944i | \(0.694560\pi\) | |||||||
\(398\) | −14.4095 | −0.722282 | ||||||||
\(399\) | −4.82392 | − | 2.17481i | −0.241498 | − | 0.108877i | ||||
\(400\) | 1.39342 | 0.0696708 | ||||||||
\(401\) | −3.11656 | − | 5.39804i | −0.155634 | − | 0.269565i | 0.777656 | − | 0.628690i | \(-0.216409\pi\) |
−0.933290 | + | 0.359125i | \(0.883075\pi\) | |||||||
\(402\) | 1.87084 | − | 3.24040i | 0.0933092 | − | 0.161616i | ||||
\(403\) | 0.393417 | − | 0.681418i | 0.0195975 | − | 0.0339439i | ||||
\(404\) | −2.69671 | − | 4.67084i | −0.134166 | − | 0.232383i | ||||
\(405\) | 2.52852 | 0.125643 | ||||||||
\(406\) | 1.21734 | + | 12.1269i | 0.0604154 | + | 0.601849i | ||||
\(407\) | 38.9036 | 1.92838 | ||||||||
\(408\) | 3.41196 | + | 5.90969i | 0.168917 | + | 0.292573i | ||||
\(409\) | −0.184646 | + | 0.319815i | −0.00913013 | + | 0.0158139i | −0.870554 | − | 0.492072i | \(-0.836240\pi\) |
0.861424 | + | 0.507886i | \(0.169573\pi\) | |||||||
\(410\) | 3.86490 | − | 6.69420i | 0.190874 | − | 0.330603i | ||||
\(411\) | −8.76440 | − | 15.1804i | −0.432316 | − | 0.748793i | ||||
\(412\) | −18.1512 | −0.894244 | ||||||||
\(413\) | 21.7220 | − | 15.6274i | 1.06887 | − | 0.768976i | ||||
\(414\) | −1.00000 | −0.0491473 | ||||||||
\(415\) | 17.2544 | + | 29.8855i | 0.846986 | + | 1.46702i | ||||
\(416\) | −0.196708 | + | 0.340709i | −0.00964443 | + | 0.0167046i | ||||
\(417\) | 6.52063 | − | 11.2941i | 0.319317 | − | 0.553073i | ||||
\(418\) | 4.29540 | + | 7.43985i | 0.210095 | + | 0.363895i | ||||
\(419\) | 30.4837 | 1.48922 | 0.744612 | − | 0.667498i | \(-0.232635\pi\) | ||||
0.744612 | + | 0.667498i | \(0.232635\pi\) | |||||||
\(420\) | −5.43050 | + | 3.90686i | −0.264981 | + | 0.190635i | ||||
\(421\) | 34.2954 | 1.67146 | 0.835728 | − | 0.549144i | \(-0.185046\pi\) | ||||
0.835728 | + | 0.549144i | \(0.185046\pi\) | |||||||
\(422\) | −7.59869 | − | 13.1613i | −0.369899 | − | 0.640683i | ||||
\(423\) | 4.79540 | − | 8.30588i | 0.233160 | − | 0.403846i | ||||
\(424\) | −0.129157 | + | 0.223706i | −0.00627240 | + | 0.0108641i | ||||
\(425\) | −4.75428 | − | 8.23466i | −0.230617 | − | 0.399440i | ||||
\(426\) | 13.8610 | 0.671568 | ||||||||
\(427\) | 0.849112 | + | 8.45873i | 0.0410914 | + | 0.409347i | ||||
\(428\) | 16.5908 | 0.801947 | ||||||||
\(429\) | 0.844941 | + | 1.46348i | 0.0407942 | + | 0.0706575i | ||||
\(430\) | −2.52852 | + | 4.37953i | −0.121936 | + | 0.211200i | ||||
\(431\) | −16.0983 | + | 27.8831i | −0.775428 | + | 1.34308i | 0.159126 | + | 0.987258i | \(0.449132\pi\) |
−0.934554 | + | 0.355822i | \(0.884201\pi\) | |||||||
\(432\) | 0.500000 | + | 0.866025i | 0.0240563 | + | 0.0416667i | ||||
\(433\) | −22.5592 | −1.08413 | −0.542064 | − | 0.840337i | \(-0.682357\pi\) | ||||
−0.542064 | + | 0.840337i | \(0.682357\pi\) | |||||||
\(434\) | 4.82392 | + | 2.17481i | 0.231556 | + | 0.104394i | ||||
\(435\) | −11.6478 | −0.558471 | ||||||||
\(436\) | −7.28280 | − | 12.6142i | −0.348783 | − | 0.604110i | ||||
\(437\) | −1.00000 | + | 1.73205i | −0.0478365 | + | 0.0828552i | ||||
\(438\) | 2.10658 | − | 3.64871i | 0.100656 | − | 0.174342i | ||||
\(439\) | −2.97481 | − | 5.15252i | −0.141980 | − | 0.245916i | 0.786262 | − | 0.617893i | \(-0.212013\pi\) |
−0.928242 | + | 0.371977i | \(0.878680\pi\) | |||||||
\(440\) | 10.8610 | 0.517778 | ||||||||
\(441\) | 2.22523 | − | 6.63689i | 0.105963 | − | 0.316043i | ||||
\(442\) | 2.68465 | 0.127696 | ||||||||
\(443\) | −7.62197 | − | 13.2016i | −0.362131 | − | 0.627229i | 0.626180 | − | 0.779678i | \(-0.284617\pi\) |
−0.988311 | + | 0.152449i | \(0.951284\pi\) | |||||||
\(444\) | 4.52852 | − | 7.84363i | 0.214914 | − | 0.372242i | ||||
\(445\) | 10.4557 | − | 18.1098i | 0.495648 | − | 0.858487i | ||||
\(446\) | 10.5856 | + | 18.3347i | 0.501241 | + | 0.868175i | ||||
\(447\) | 0.0622786 | 0.00294568 | ||||||||
\(448\) | −2.41196 | − | 1.08740i | −0.113954 | − | 0.0513750i | ||||
\(449\) | −22.5488 | −1.06414 | −0.532071 | − | 0.846700i | \(-0.678586\pi\) | ||||
−0.532071 | + | 0.846700i | \(0.678586\pi\) | |||||||
\(450\) | −0.696708 | − | 1.20673i | −0.0328432 | − | 0.0568860i | ||||
\(451\) | 6.56561 | − | 11.3720i | 0.309162 | − | 0.535485i | ||||
\(452\) | 4.55966 | − | 7.89756i | 0.214468 | − | 0.371470i | ||||
\(453\) | −1.07806 | − | 1.86726i | −0.0506518 | − | 0.0877315i | ||||
\(454\) | −2.40948 | −0.113083 | ||||||||
\(455\) | 0.262876 | + | 2.61873i | 0.0123238 | + | 0.122768i | ||||
\(456\) | 2.00000 | 0.0936586 | ||||||||
\(457\) | −1.05704 | − | 1.83085i | −0.0494463 | − | 0.0856435i | 0.840243 | − | 0.542210i | \(-0.182412\pi\) |
−0.889689 | + | 0.456567i | \(0.849079\pi\) | |||||||
\(458\) | −5.30800 | + | 9.19372i | −0.248026 | + | 0.429594i | ||||
\(459\) | 3.41196 | − | 5.90969i | 0.159257 | − | 0.275841i | ||||
\(460\) | 1.26426 | + | 2.18976i | 0.0589464 | + | 0.102098i | ||||
\(461\) | 6.00000 | 0.279448 | 0.139724 | − | 0.990190i | \(-0.455378\pi\) | ||||
0.139724 | + | 0.990190i | \(0.455378\pi\) | |||||||
\(462\) | −9.22523 | + | 6.63689i | −0.429197 | + | 0.308776i | ||||
\(463\) | −2.42633 | −0.112761 | −0.0563806 | − | 0.998409i | \(-0.517956\pi\) | ||||
−0.0563806 | + | 0.998409i | \(0.517956\pi\) | |||||||
\(464\) | −2.30329 | − | 3.98942i | −0.106928 | − | 0.185204i | ||||
\(465\) | −2.52852 | + | 4.37953i | −0.117257 | + | 0.203096i | ||||
\(466\) | −6.59080 | + | 11.4156i | −0.305313 | + | 0.528817i | ||||
\(467\) | 9.89356 | + | 17.1361i | 0.457819 | + | 0.792966i | 0.998845 | − | 0.0480395i | \(-0.0152973\pi\) |
−0.541026 | + | 0.841006i | \(0.681964\pi\) | |||||||
\(468\) | 0.393417 | 0.0181857 | ||||||||
\(469\) | 8.03602 | − | 5.78134i | 0.371069 | − | 0.266958i | ||||
\(470\) | −24.2505 | −1.11859 | ||||||||
\(471\) | 5.54112 | + | 9.59750i | 0.255321 | + | 0.442229i | ||||
\(472\) | −5.05704 | + | 8.75905i | −0.232769 | + | 0.403168i | ||||
\(473\) | −4.29540 | + | 7.43985i | −0.197503 | + | 0.342085i | ||||
\(474\) | 1.85230 | + | 3.20828i | 0.0850790 | + | 0.147361i | ||||
\(475\) | −2.78683 | −0.127869 | ||||||||
\(476\) | 1.80329 | + | 17.9641i | 0.0826537 | + | 0.823384i | ||||
\(477\) | 0.258313 | 0.0118273 | ||||||||
\(478\) | −2.12721 | − | 3.68444i | −0.0972964 | − | 0.168522i | ||||
\(479\) | −11.0623 | + | 19.1604i | −0.505448 | + | 0.875462i | 0.494532 | + | 0.869160i | \(0.335340\pi\) |
−0.999980 | + | 0.00630275i | \(0.997994\pi\) | |||||||
\(480\) | 1.26426 | − | 2.18976i | 0.0577053 | − | 0.0999486i | ||||
\(481\) | −1.78160 | − | 3.08582i | −0.0812338 | − | 0.140701i | ||||
\(482\) | 15.5338 | 0.707543 | ||||||||
\(483\) | −2.41196 | − | 1.08740i | −0.109748 | − | 0.0494786i | ||||
\(484\) | 7.45046 | 0.338657 | ||||||||
\(485\) | 10.1141 | + | 17.5181i | 0.459257 | + | 0.795456i | ||||
\(486\) | 0.500000 | − | 0.866025i | 0.0226805 | − | 0.0392837i | ||||
\(487\) | −4.27438 | + | 7.40344i | −0.193691 | + | 0.335482i | −0.946470 | − | 0.322790i | \(-0.895379\pi\) |
0.752780 | + | 0.658272i | \(0.228712\pi\) | |||||||
\(488\) | −1.60658 | − | 2.78268i | −0.0727266 | − | 0.125966i | ||||
\(489\) | −12.2544 | −0.554164 | ||||||||
\(490\) | −17.3465 | + | 3.51804i | −0.783635 | + | 0.158929i | ||||
\(491\) | 22.4360 | 1.01252 | 0.506262 | − | 0.862380i | \(-0.331027\pi\) | ||||
0.506262 | + | 0.862380i | \(0.331027\pi\) | |||||||
\(492\) | −1.52852 | − | 2.64748i | −0.0689110 | − | 0.119357i | ||||
\(493\) | −15.7175 | + | 27.2235i | −0.707880 | + | 1.22608i | ||||
\(494\) | 0.393417 | − | 0.681418i | 0.0177007 | − | 0.0306584i | ||||
\(495\) | −5.43050 | − | 9.40591i | −0.244083 | − | 0.422764i | ||||
\(496\) | −2.00000 | −0.0898027 | ||||||||
\(497\) | 33.4322 | + | 15.0725i | 1.49964 | + | 0.676095i | ||||
\(498\) | 13.6478 | 0.611574 | ||||||||
\(499\) | 18.2465 | + | 31.6039i | 0.816827 | + | 1.41479i | 0.908009 | + | 0.418952i | \(0.137602\pi\) |
−0.0911817 | + | 0.995834i | \(0.529064\pi\) | |||||||
\(500\) | 4.55966 | − | 7.89756i | 0.203914 | − | 0.353190i | ||||
\(501\) | 2.40987 | − | 4.17403i | 0.107665 | − | 0.186482i | ||||
\(502\) | 10.7133 | + | 18.5560i | 0.478158 | + | 0.828194i | ||||
\(503\) | 38.4585 | 1.71478 | 0.857389 | − | 0.514669i | \(-0.172085\pi\) | ||||
0.857389 | + | 0.514669i | \(0.172085\pi\) | |||||||
\(504\) | 0.264260 | + | 2.63252i | 0.0117711 | + | 0.117262i | ||||
\(505\) | 13.6374 | 0.606855 | ||||||||
\(506\) | 2.14770 | + | 3.71993i | 0.0954769 | + | 0.165371i | ||||
\(507\) | −6.42261 | + | 11.1243i | −0.285238 | + | 0.494047i | ||||
\(508\) | −3.13510 | + | 5.43016i | −0.139098 | + | 0.240924i | ||||
\(509\) | −11.2875 | − | 19.5505i | −0.500310 | − | 0.866562i | −1.00000 | 0.000357978i | \(-0.999886\pi\) | |
0.499690 | − | 0.866204i | \(-0.333447\pi\) | |||||||
\(510\) | −17.2544 | −0.764039 | ||||||||
\(511\) | 9.04862 | − | 6.50983i | 0.400287 | − | 0.287978i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −1.00000 | − | 1.73205i | −0.0441511 | − | 0.0764719i | ||||
\(514\) | −9.76688 | + | 16.9167i | −0.430799 | + | 0.746165i | ||||
\(515\) | 22.9478 | − | 39.7468i | 1.01120 | − | 1.75145i | ||||
\(516\) | 1.00000 | + | 1.73205i | 0.0440225 | + | 0.0762493i | ||||
\(517\) | −41.1963 | −1.81181 | ||||||||
\(518\) | 19.4518 | − | 13.9942i | 0.854663 | − | 0.614869i | ||||
\(519\) | −22.9593 | −1.00780 | ||||||||
\(520\) | −0.497381 | − | 0.861490i | −0.0218116 | − | 0.0377788i | ||||
\(521\) | −8.76759 | + | 15.1859i | −0.384115 | + | 0.665307i | −0.991646 | − | 0.128989i | \(-0.958827\pi\) |
0.607531 | + | 0.794296i | \(0.292160\pi\) | |||||||
\(522\) | −2.30329 | + | 3.98942i | −0.100812 | + | 0.174612i | ||||
\(523\) | −10.1505 | − | 17.5811i | −0.443849 | − | 0.768768i | 0.554123 | − | 0.832435i | \(-0.313054\pi\) |
−0.997971 | + | 0.0636667i | \(0.979721\pi\) | |||||||
\(524\) | −19.0983 | −0.834313 | ||||||||
\(525\) | −0.368225 | − | 3.66820i | −0.0160706 | − | 0.160093i | ||||
\(526\) | 17.8040 | 0.776290 | ||||||||
\(527\) | 6.82392 | + | 11.8194i | 0.297255 | + | 0.514860i | ||||
\(528\) | 2.14770 | − | 3.71993i | 0.0934666 | − | 0.161889i | ||||
\(529\) | −0.500000 | + | 0.866025i | −0.0217391 | + | 0.0376533i | ||||
\(530\) | −0.326575 | − | 0.565644i | −0.0141855 | − | 0.0245700i | ||||
\(531\) | 10.1141 | 0.438914 | ||||||||
\(532\) | 4.82392 | + | 2.17481i | 0.209143 | + | 0.0942899i | ||||
\(533\) | −1.20269 | −0.0520944 | ||||||||
\(534\) | −4.13510 | − | 7.16221i | −0.178943 | − | 0.309939i | ||||
\(535\) | −20.9751 | + | 36.3299i | −0.906832 | + | 1.57068i | ||||
\(536\) | −1.87084 | + | 3.24040i | −0.0808081 | + | 0.139964i | ||||
\(537\) | 10.9226 | + | 18.9185i | 0.471345 | + | 0.816394i | ||||
\(538\) | −19.6321 | −0.846398 | ||||||||
\(539\) | −29.4679 | + | 5.97637i | −1.26927 | + | 0.257420i | ||||
\(540\) | −2.52852 | −0.108810 | ||||||||
\(541\) | −15.9016 | − | 27.5424i | −0.683663 | − | 1.18414i | −0.973855 | − | 0.227170i | \(-0.927053\pi\) |
0.290192 | − | 0.956968i | \(-0.406281\pi\) | |||||||
\(542\) | −4.68882 | + | 8.12127i | −0.201402 | + | 0.348838i | ||||
\(543\) | −11.0497 | + | 19.1386i | −0.474187 | + | 0.821316i | ||||
\(544\) | −3.41196 | − | 5.90969i | −0.146287 | − | 0.253376i | ||||
\(545\) | 36.8294 | 1.57760 | ||||||||
\(546\) | 0.948906 | + | 0.427803i | 0.0406094 | + | 0.0183083i | ||||
\(547\) | 29.5817 | 1.26482 | 0.632410 | − | 0.774633i | \(-0.282066\pi\) | ||||
0.632410 | + | 0.774633i | \(0.282066\pi\) | |||||||
\(548\) | 8.76440 | + | 15.1804i | 0.374397 | + | 0.648474i | ||||
\(549\) | −1.60658 | + | 2.78268i | −0.0685673 | + | 0.118762i | ||||
\(550\) | −2.99264 | + | 5.18341i | −0.127607 | + | 0.221021i | ||||
\(551\) | 4.60658 | + | 7.97884i | 0.196247 | + | 0.339910i | ||||
\(552\) | 1.00000 | 0.0425628 | ||||||||
\(553\) | 0.978979 | + | 9.75244i | 0.0416304 | + | 0.414716i | ||||
\(554\) | −11.9272 | −0.506737 | ||||||||
\(555\) | 11.4505 | + | 19.8328i | 0.486045 | + | 0.841854i | ||||
\(556\) | −6.52063 | + | 11.2941i | −0.276536 | + | 0.478975i | ||||
\(557\) | 10.7511 | − | 18.6214i | 0.455539 | − | 0.789016i | −0.543180 | − | 0.839616i | \(-0.682780\pi\) |
0.998719 | + | 0.0506001i | \(0.0161134\pi\) | |||||||
\(558\) | 1.00000 | + | 1.73205i | 0.0423334 | + | 0.0733236i | ||||
\(559\) | 0.786834 | 0.0332795 | ||||||||
\(560\) | 5.43050 | − | 3.90686i | 0.229481 | − | 0.165095i | ||||
\(561\) | −29.3115 | −1.23753 | ||||||||
\(562\) | 5.33914 | + | 9.24765i | 0.225218 | + | 0.390089i | ||||
\(563\) | 15.7333 | − | 27.2508i | 0.663078 | − | 1.14848i | −0.316725 | − | 0.948518i | \(-0.602583\pi\) |
0.979803 | − | 0.199967i | \(-0.0640835\pi\) | |||||||
\(564\) | −4.79540 | + | 8.30588i | −0.201923 | + | 0.349740i | ||||
\(565\) | 11.5292 | + | 19.9692i | 0.485037 | + | 0.840108i | ||||
\(566\) | −11.2334 | −0.472175 | ||||||||
\(567\) | 2.14770 | − | 1.54512i | 0.0901949 | − | 0.0648888i | ||||
\(568\) | −13.8610 | −0.581595 | ||||||||
\(569\) | 18.7360 | + | 32.4517i | 0.785455 | + | 1.36045i | 0.928727 | + | 0.370764i | \(0.120904\pi\) |
−0.143272 | + | 0.989683i | \(0.545762\pi\) | |||||||
\(570\) | −2.52852 | + | 4.37953i | −0.105908 | + | 0.183438i | ||||
\(571\) | −14.1042 | + | 24.4293i | −0.590244 | + | 1.02233i | 0.403955 | + | 0.914779i | \(0.367635\pi\) |
−0.994199 | + | 0.107554i | \(0.965698\pi\) | |||||||
\(572\) | −0.844941 | − | 1.46348i | −0.0353288 | − | 0.0611912i | ||||
\(573\) | 8.27021 | 0.345493 | ||||||||
\(574\) | −0.807855 | − | 8.04773i | −0.0337192 | − | 0.335906i | ||||
\(575\) | −1.39342 | −0.0581095 | ||||||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | −1.43840 | + | 2.49137i | −0.0598812 | + | 0.103717i | −0.894412 | − | 0.447244i | \(-0.852406\pi\) |
0.834531 | + | 0.550961i | \(0.185739\pi\) | |||||||
\(578\) | −14.7829 | + | 25.6048i | −0.614889 | + | 1.06502i | ||||
\(579\) | −3.25375 | − | 5.63566i | −0.135221 | − | 0.234210i | ||||
\(580\) | 11.6478 | 0.483650 | ||||||||
\(581\) | 32.9180 | + | 14.8407i | 1.36567 | + | 0.615697i | ||||
\(582\) | 8.00000 | 0.331611 | ||||||||
\(583\) | −0.554779 | − | 0.960905i | −0.0229766 | − | 0.0397966i | ||||
\(584\) | −2.10658 | + | 3.64871i | −0.0871710 | + | 0.150985i | ||||
\(585\) | −0.497381 | + | 0.861490i | −0.0205642 | + | 0.0356182i | ||||
\(586\) | −11.0882 | − | 19.2053i | −0.458049 | − | 0.793363i | ||||
\(587\) | −19.8873 | −0.820835 | −0.410418 | − | 0.911898i | \(-0.634617\pi\) | ||||
−0.410418 | + | 0.911898i | \(0.634617\pi\) | |||||||
\(588\) | −2.22523 | + | 6.63689i | −0.0917669 | + | 0.273701i | ||||
\(589\) | 4.00000 | 0.164817 | ||||||||
\(590\) | −12.7868 | − | 22.1474i | −0.526426 | − | 0.911796i | ||||
\(591\) | 4.09013 | − | 7.08430i | 0.168245 | − | 0.291409i | ||||
\(592\) | −4.52852 | + | 7.84363i | −0.186121 | + | 0.322371i | ||||
\(593\) | 0.553713 | + | 0.959059i | 0.0227383 | + | 0.0393838i | 0.877171 | − | 0.480179i | \(-0.159428\pi\) |
−0.854432 | + | 0.519563i | \(0.826095\pi\) | |||||||
\(594\) | −4.29540 | −0.176242 | ||||||||
\(595\) | −41.6170 | − | 18.7625i | −1.70613 | − | 0.769189i | ||||
\(596\) | −0.0622786 | −0.00255103 | ||||||||
\(597\) | −7.20474 | − | 12.4790i | −0.294870 | − | 0.510731i | ||||
\(598\) | 0.196708 | − | 0.340709i | 0.00804401 | − | 0.0139326i | ||||
\(599\) | 14.8735 | − | 25.7616i | 0.607713 | − | 1.05259i | −0.383903 | − | 0.923373i | \(-0.625420\pi\) |
0.991616 | − | 0.129217i | \(-0.0412463\pi\) | |||||||
\(600\) | 0.696708 | + | 1.20673i | 0.0284430 | + | 0.0492647i | ||||
\(601\) | −3.88592 | −0.158510 | −0.0792549 | − | 0.996854i | \(-0.525254\pi\) | ||||
−0.0792549 | + | 0.996854i | \(0.525254\pi\) | |||||||
\(602\) | 0.528521 | + | 5.26504i | 0.0215409 | + | 0.214587i | ||||
\(603\) | 3.74169 | 0.152373 | ||||||||
\(604\) | 1.07806 | + | 1.86726i | 0.0438657 | + | 0.0759777i | ||||
\(605\) | −9.41932 | + | 16.3147i | −0.382950 | + | 0.663288i | ||||
\(606\) | 2.69671 | − | 4.67084i | 0.109546 | − | 0.189740i | ||||
\(607\) | 0.978979 | + | 1.69564i | 0.0397355 | + | 0.0688240i | 0.885209 | − | 0.465193i | \(-0.154015\pi\) |
−0.845474 | + | 0.534017i | \(0.820682\pi\) | |||||||
\(608\) | −2.00000 | −0.0811107 | ||||||||
\(609\) | −9.89356 | + | 7.11771i | −0.400907 | + | 0.288424i | ||||
\(610\) | 8.12456 | 0.328954 | ||||||||
\(611\) | 1.88659 | + | 3.26767i | 0.0763233 | + | 0.132196i | ||||
\(612\) | −3.41196 | + | 5.90969i | −0.137920 | + | 0.238885i | ||||
\(613\) | 1.97162 | − | 3.41495i | 0.0796330 | − | 0.137928i | −0.823459 | − | 0.567376i | \(-0.807958\pi\) |
0.903092 | + | 0.429448i | \(0.141292\pi\) | |||||||
\(614\) | 4.00789 | + | 6.94187i | 0.161745 | + | 0.280151i | ||||
\(615\) | 7.72979 | 0.311695 | ||||||||
\(616\) | 9.22523 | − | 6.63689i | 0.371695 | − | 0.267408i | ||||
\(617\) | −20.8876 | −0.840904 | −0.420452 | − | 0.907315i | \(-0.638128\pi\) | ||||
−0.420452 | + | 0.907315i | \(0.638128\pi\) | |||||||
\(618\) | −9.07558 | − | 15.7194i | −0.365074 | − | 0.632326i | ||||
\(619\) | −14.6009 | + | 25.2895i | −0.586860 | + | 1.01647i | 0.407780 | + | 0.913080i | \(0.366303\pi\) |
−0.994641 | + | 0.103392i | \(0.967030\pi\) | |||||||
\(620\) | 2.52852 | − | 4.37953i | 0.101548 | − | 0.175886i | ||||
\(621\) | −0.500000 | − | 0.866025i | −0.0200643 | − | 0.0347524i | ||||
\(622\) | 21.5908 | 0.865712 | ||||||||
\(623\) | −2.18549 | − | 21.7715i | −0.0875597 | − | 0.872257i | ||||
\(624\) | −0.393417 | −0.0157493 | ||||||||
\(625\) | 15.0127 | + | 26.0028i | 0.600509 | + | 1.04011i | ||||
\(626\) | −6.59080 | + | 11.4156i | −0.263421 | + | 0.456259i | ||||
\(627\) | −4.29540 | + | 7.43985i | −0.171542 | + | 0.297119i | ||||
\(628\) | −5.54112 | − | 9.59750i | −0.221115 | − | 0.382982i | ||||
\(629\) | 61.8045 | 2.46431 | ||||||||
\(630\) | −6.09869 | − | 2.74952i | −0.242978 | − | 0.109544i | ||||
\(631\) | −16.2653 | −0.647509 | −0.323755 | − | 0.946141i | \(-0.604945\pi\) | ||||
−0.323755 | + | 0.946141i | \(0.604945\pi\) | |||||||
\(632\) | −1.85230 | − | 3.20828i | −0.0736805 | − | 0.127618i | ||||
\(633\) | 7.59869 | − | 13.1613i | 0.302021 | − | 0.523115i | ||||
\(634\) | 7.11408 | − | 12.3220i | 0.282536 | − | 0.489367i | ||||
\(635\) | −7.92717 | − | 13.7303i | −0.314580 | − | 0.544869i | ||||
\(636\) | −0.258313 | −0.0102428 | ||||||||
\(637\) | 1.82353 | + | 2.06369i | 0.0722508 | + | 0.0817663i | ||||
\(638\) | 19.7871 | 0.783379 | ||||||||
\(639\) | 6.93050 | + | 12.0040i | 0.274166 | + | 0.474870i | ||||
\(640\) | −1.26426 | + | 2.18976i | −0.0499743 | + | 0.0865580i | ||||
\(641\) | 12.3087 | − | 21.3193i | 0.486165 | − | 0.842062i | −0.513709 | − | 0.857965i | \(-0.671729\pi\) |
0.999874 | + | 0.0159027i | \(0.00506219\pi\) | |||||||
\(642\) | 8.29540 | + | 14.3681i | 0.327393 | + | 0.567062i | ||||
\(643\) | −15.2132 | −0.599949 | −0.299974 | − | 0.953947i | \(-0.596978\pi\) | ||||
−0.299974 | + | 0.953947i | \(0.596978\pi\) | |||||||
\(644\) | 2.41196 | + | 1.08740i | 0.0950445 | + | 0.0428497i | ||||
\(645\) | −5.05704 | −0.199121 | ||||||||
\(646\) | 6.82392 | + | 11.8194i | 0.268484 | + | 0.465027i | ||||
\(647\) | −5.53641 | + | 9.58935i | −0.217659 | + | 0.376996i | −0.954092 | − | 0.299514i | \(-0.903175\pi\) |
0.736433 | + | 0.676511i | \(0.236509\pi\) | |||||||
\(648\) | −0.500000 | + | 0.866025i | −0.0196419 | + | 0.0340207i | ||||
\(649\) | −21.7220 | − | 37.6236i | −0.852664 | − | 1.47686i | ||||
\(650\) | 0.548194 | 0.0215019 | ||||||||
\(651\) | 0.528521 | + | 5.26504i | 0.0207144 | + | 0.206353i | ||||
\(652\) | 12.2544 | 0.479920 | ||||||||
\(653\) | −20.0292 | − | 34.6916i | −0.783803 | − | 1.35759i | −0.929712 | − | 0.368288i | \(-0.879944\pi\) |
0.145909 | − | 0.989298i | \(-0.453389\pi\) | |||||||
\(654\) | 7.28280 | − | 12.6142i | 0.284780 | − | 0.493254i | ||||
\(655\) | 24.1452 | − | 41.8208i | 0.943432 | − | 1.63407i | ||||
\(656\) | 1.52852 | + | 2.64748i | 0.0596787 | + | 0.103367i | ||||
\(657\) | 4.21317 | 0.164371 | ||||||||
\(658\) | −20.5982 | + | 14.8189i | −0.803000 | + | 0.577701i | ||||
\(659\) | −42.3380 | −1.64925 | −0.824627 | − | 0.565676i | \(-0.808615\pi\) | ||||
−0.824627 | + | 0.565676i | \(0.808615\pi\) | |||||||
\(660\) | 5.43050 | + | 9.40591i | 0.211382 | + | 0.366124i | ||||
\(661\) | 7.74905 | − | 13.4217i | 0.301403 | − | 0.522045i | −0.675051 | − | 0.737771i | \(-0.735878\pi\) |
0.976454 | + | 0.215726i | \(0.0692117\pi\) | |||||||
\(662\) | 10.7987 | − | 18.7039i | 0.419704 | − | 0.726950i | ||||
\(663\) | 1.34232 | + | 2.32497i | 0.0521315 | + | 0.0902944i | ||||
\(664\) | −13.6478 | −0.529639 | ||||||||
\(665\) | −10.8610 | + | 7.81372i | −0.421172 | + | 0.303003i | ||||
\(666\) | 9.05704 | 0.350953 | ||||||||
\(667\) | 2.30329 | + | 3.98942i | 0.0891838 | + | 0.154471i | ||||
\(668\) | −2.40987 | + | 4.17403i | −0.0932409 | + | 0.161498i | ||||
\(669\) | −10.5856 | + | 18.3347i | −0.409261 | + | 0.708862i | ||||
\(670\) | −4.73047 | − | 8.19341i | −0.182754 | − | 0.316539i | ||||
\(671\) | 13.8018 | 0.532814 | ||||||||
\(672\) | −0.264260 | − | 2.63252i | −0.0101941 | − | 0.101552i | ||||
\(673\) | −37.1875 | −1.43347 | −0.716736 | − | 0.697345i | \(-0.754365\pi\) | ||||
−0.716736 | + | 0.697345i | \(0.754365\pi\) | |||||||
\(674\) | −6.60658 | − | 11.4429i | −0.254476 | − | 0.440765i | ||||
\(675\) | 0.696708 | − | 1.20673i | 0.0268163 | − | 0.0464472i | ||||
\(676\) | 6.42261 | − | 11.1243i | 0.247024 | − | 0.427857i | ||||
\(677\) | 12.3584 | + | 21.4054i | 0.474971 | + | 0.822675i | 0.999589 | − | 0.0286633i | \(-0.00912505\pi\) |
−0.524618 | + | 0.851338i | \(0.675792\pi\) | |||||||
\(678\) | 9.11932 | 0.350225 | ||||||||
\(679\) | 19.2957 | + | 8.69923i | 0.740500 | + | 0.333846i | ||||
\(680\) | 17.2544 | 0.661677 | ||||||||
\(681\) | −1.20474 | − | 2.08667i | −0.0461658 | − | 0.0799615i | ||||
\(682\) | 4.29540 | − | 7.43985i | 0.164479 | − | 0.284887i | ||||
\(683\) | 21.0325 | − | 36.4294i | 0.804787 | − | 1.39393i | −0.111648 | − | 0.993748i | \(-0.535613\pi\) |
0.916435 | − | 0.400184i | \(-0.131054\pi\) | |||||||
\(684\) | 1.00000 | + | 1.73205i | 0.0382360 | + | 0.0662266i | ||||
\(685\) | −44.3219 | −1.69345 | ||||||||
\(686\) | −12.5842 | + | 13.5882i | −0.480465 | + | 0.518800i | ||||
\(687\) | −10.6160 | −0.405025 | ||||||||
\(688\) | −1.00000 | − | 1.73205i | −0.0381246 | − | 0.0660338i | ||||
\(689\) | −0.0508124 | + | 0.0880096i | −0.00193580 | + | 0.00335290i | ||||
\(690\) | −1.26426 | + | 2.18976i | −0.0481296 | + | 0.0833629i | ||||
\(691\) | 5.26232 | + | 9.11460i | 0.200188 | + | 0.346736i | 0.948589 | − | 0.316511i | \(-0.102511\pi\) |
−0.748401 | + | 0.663247i | \(0.769178\pi\) | |||||||
\(692\) | 22.9593 | 0.872782 | ||||||||
\(693\) | −10.3603 | − | 4.67084i | −0.393557 | − | 0.177430i | ||||
\(694\) | −19.4189 | −0.737131 | ||||||||
\(695\) | −16.4875 | − | 28.5573i | −0.625408 | − | 1.08324i | ||||
\(696\) | 2.30329 | − | 3.98942i | 0.0873060 | − | 0.151218i | ||||
\(697\) | 10.4305 | − | 18.0662i | 0.395083 | − | 0.684305i | ||||
\(698\) | 2.90131 | + | 5.02521i | 0.109816 | + | 0.190207i | ||||
\(699\) | −13.1816 | −0.498574 | ||||||||
\(700\) | 0.368225 | + | 3.66820i | 0.0139176 | + | 0.138645i | ||||
\(701\) | −28.1764 | −1.06421 | −0.532103 | − | 0.846679i | \(-0.678598\pi\) | ||||
−0.532103 | + | 0.846679i | \(0.678598\pi\) | |||||||
\(702\) | 0.196708 | + | 0.340709i | 0.00742428 | + | 0.0128592i | ||||
\(703\) | 9.05704 | − | 15.6873i | 0.341593 | − | 0.591656i | ||||
\(704\) | −2.14770 | + | 3.71993i | −0.0809445 | + | 0.140200i | ||||
\(705\) | −12.1253 | − | 21.0016i | −0.456664 | − | 0.790965i | ||||
\(706\) | 20.9430 | 0.788199 | ||||||||
\(707\) | 11.5834 | − | 8.33346i | 0.435640 | − | 0.313412i | ||||
\(708\) | −10.1141 | −0.380111 | ||||||||
\(709\) | 1.93036 | + | 3.34349i | 0.0724963 | + | 0.125567i | 0.899995 | − | 0.435901i | \(-0.143570\pi\) |
−0.827498 | + | 0.561468i | \(0.810237\pi\) | |||||||
\(710\) | 17.5239 | − | 30.3523i | 0.657661 | − | 1.13910i | ||||
\(711\) | −1.85230 | + | 3.20828i | −0.0694667 | + | 0.120320i | ||||
\(712\) | 4.13510 | + | 7.16221i | 0.154970 | + | 0.268415i | ||||
\(713\) | 2.00000 | 0.0749006 | ||||||||
\(714\) | −14.6557 | + | 10.5438i | −0.548477 | + | 0.394590i | ||||
\(715\) | 4.27290 | 0.159798 | ||||||||
\(716\) | −10.9226 | − | 18.9185i | −0.408197 | − | 0.707018i | ||||
\(717\) | 2.12721 | − | 3.68444i | 0.0794422 | − | 0.137598i | ||||
\(718\) | 2.35244 | − | 4.07455i | 0.0877923 | − | 0.152061i | ||||
\(719\) | 15.2590 | + | 26.4293i | 0.569064 | + | 0.985648i | 0.996659 | + | 0.0816775i | \(0.0260277\pi\) |
−0.427595 | + | 0.903971i | \(0.640639\pi\) | |||||||
\(720\) | 2.52852 | 0.0942324 | ||||||||
\(721\) | −4.79663 | − | 47.7833i | −0.178636 | − | 1.77954i | ||||
\(722\) | −15.0000 | −0.558242 | ||||||||
\(723\) | 7.76688 | + | 13.4526i | 0.288853 | + | 0.500309i | ||||
\(724\) | 11.0497 | − | 19.1386i | 0.410658 | − | 0.711281i | ||||
\(725\) | −3.20945 | + | 5.55892i | −0.119196 | + | 0.206453i | ||||
\(726\) | 3.72523 | + | 6.45229i | 0.138256 | + | 0.239467i | ||||
\(727\) | −14.3591 | −0.532549 | −0.266275 | − | 0.963897i | \(-0.585793\pi\) | ||||
−0.266275 | + | 0.963897i | \(0.585793\pi\) | |||||||
\(728\) | −0.948906 | − | 0.427803i | −0.0351688 | − | 0.0158554i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −5.32654 | − | 9.22584i | −0.197144 | − | 0.341464i | ||||
\(731\) | −6.82392 | + | 11.8194i | −0.252392 | + | 0.437155i | ||||
\(732\) | 1.60658 | − | 2.78268i | 0.0593810 | − | 0.102851i | ||||
\(733\) | 5.95555 | + | 10.3153i | 0.219973 | + | 0.381005i | 0.954800 | − | 0.297250i | \(-0.0960696\pi\) |
−0.734826 | + | 0.678256i | \(0.762736\pi\) | |||||||
\(734\) | −9.43991 | −0.348434 | ||||||||
\(735\) | −11.7200 | − | 13.2635i | −0.432297 | − | 0.489231i | ||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | −8.03602 | − | 13.9188i | −0.296011 | − | 0.512705i | ||||
\(738\) | 1.52852 | − | 2.64748i | 0.0562656 | − | 0.0974549i | ||||
\(739\) | 20.5619 | − | 35.6142i | 0.756381 | − | 1.31009i | −0.188304 | − | 0.982111i | \(-0.560299\pi\) |
0.944685 | − | 0.327980i | \(-0.106368\pi\) | |||||||
\(740\) | −11.4505 | − | 19.8328i | −0.420927 | − | 0.729067i | ||||
\(741\) | 0.786834 | 0.0289051 | ||||||||
\(742\) | −0.623041 | − | 0.280891i | −0.0228726 | − | 0.0103118i | ||||
\(743\) | 10.8610 | 0.398452 | 0.199226 | − | 0.979954i | \(-0.436157\pi\) | ||||
0.199226 | + | 0.979954i | \(0.436157\pi\) | |||||||
\(744\) | −1.00000 | − | 1.73205i | −0.0366618 | − | 0.0635001i | ||||
\(745\) | 0.0787364 | − | 0.136375i | 0.00288468 | − | 0.00499641i | ||||
\(746\) | −5.83652 | + | 10.1091i | −0.213690 | + | 0.370122i | ||||
\(747\) | 6.82392 | + | 11.8194i | 0.249674 | + | 0.432448i | ||||
\(748\) | 29.3115 | 1.07173 | ||||||||
\(749\) | 4.38429 | + | 43.6756i | 0.160198 | + | 1.59587i | ||||
\(750\) | 9.11932 | 0.332990 | ||||||||
\(751\) | 26.3367 | + | 45.6164i | 0.961038 | + | 1.66457i | 0.719902 | + | 0.694076i | \(0.244187\pi\) |
0.241136 | + | 0.970491i | \(0.422480\pi\) | |||||||
\(752\) | 4.79540 | − | 8.30588i | 0.174870 | − | 0.302884i | ||||
\(753\) | −10.7133 | + | 18.5560i | −0.390415 | + | 0.676218i | ||||
\(754\) | −0.906154 | − | 1.56950i | −0.0330002 | − | 0.0571580i | ||||
\(755\) | −5.45181 | −0.198412 | ||||||||
\(756\) | −2.14770 | + | 1.54512i | −0.0781111 | + | 0.0561953i | ||||
\(757\) | 16.0000 | 0.581530 | 0.290765 | − | 0.956795i | \(-0.406090\pi\) | ||||
0.290765 | + | 0.956795i | \(0.406090\pi\) | |||||||
\(758\) | −4.71472 | − | 8.16613i | −0.171246 | − | 0.296607i | ||||
\(759\) | −2.14770 | + | 3.71993i | −0.0779566 | + | 0.135025i | ||||
\(760\) | 2.52852 | − | 4.37953i | 0.0917191 | − | 0.158862i | ||||
\(761\) | −3.68882 | − | 6.38922i | −0.133719 | − | 0.231609i | 0.791388 | − | 0.611314i | \(-0.209359\pi\) |
−0.925108 | + | 0.379705i | \(0.876025\pi\) | |||||||
\(762\) | −6.27021 | −0.227146 | ||||||||
\(763\) | 31.2826 | − | 22.5056i | 1.13250 | − | 0.814756i | ||||
\(764\) | −8.27021 | −0.299206 | ||||||||
\(765\) | −8.62721 | − | 14.9428i | −0.311918 | − | 0.540257i | ||||
\(766\) | 11.7049 | − | 20.2735i | 0.422915 | − | 0.732510i | ||||
\(767\) | −1.98953 | + | 3.44596i | −0.0718376 | + | 0.124426i | ||||
\(768\) | 0.500000 | + | 0.866025i | 0.0180422 | + | 0.0312500i | ||||
\(769\) | −26.1462 | −0.942857 | −0.471428 | − | 0.881904i | \(-0.656261\pi\) | ||||
−0.471428 | + | 0.881904i | \(0.656261\pi\) | |||||||
\(770\) | 2.87013 | + | 28.5918i | 0.103432 | + | 1.03038i | ||||
\(771\) | −19.5338 | −0.703491 | ||||||||
\(772\) | 3.25375 | + | 5.63566i | 0.117105 | + | 0.202832i | ||||
\(773\) | −11.3794 | + | 19.7097i | −0.409289 | + | 0.708909i | −0.994810 | − | 0.101748i | \(-0.967557\pi\) |
0.585521 | + | 0.810657i | \(0.300890\pi\) | |||||||
\(774\) | −1.00000 | + | 1.73205i | −0.0359443 | + | 0.0622573i | ||||
\(775\) | 1.39342 | + | 2.41347i | 0.0500530 | + | 0.0866944i | ||||
\(776\) | −8.00000 | −0.287183 | ||||||||
\(777\) | 21.8452 | + | 9.84867i | 0.783693 | + | 0.353319i | ||||
\(778\) | −22.0742 | −0.791397 | ||||||||
\(779\) | −3.05704 | − | 5.29495i | −0.109530 | − | 0.189711i | ||||
\(780\) | 0.497381 | − | 0.861490i | 0.0178091 | − | 0.0308463i | ||||
\(781\) | 29.7693 | − | 51.5619i | 1.06523 | − | 1.84503i | ||||
\(782\) | 3.41196 | + | 5.90969i | 0.122011 | + | 0.211330i | ||||
\(783\) | −4.60658 | −0.164626 | ||||||||
\(784\) | 2.22523 | − | 6.63689i | 0.0794725 | − | 0.237032i | ||||
\(785\) | 28.0217 | 1.00014 | ||||||||
\(786\) | −9.54915 | − | 16.5396i | −0.340607 | − | 0.589948i | ||||
\(787\) | 2.79802 | − | 4.84631i | 0.0997386 | − | 0.172752i | −0.811838 | − | 0.583883i | \(-0.801533\pi\) |
0.911576 | + | 0.411131i | \(0.134866\pi\) | |||||||
\(788\) | −4.09013 | + | 7.08430i | −0.145705 | + | 0.252368i | ||||
\(789\) | 8.90198 | + | 15.4187i | 0.316919 | + | 0.548920i | ||||
\(790\) | 9.36716 | 0.333269 | ||||||||
\(791\) | 21.9954 | + | 9.91639i | 0.782068 | + | 0.352586i | ||||
\(792\) | 4.29540 | 0.152630 | ||||||||
\(793\) | −0.632057 | − | 1.09475i | −0.0224450 | − | 0.0388759i | ||||
\(794\) | 8.41405 | − | 14.5736i | 0.298603 | − | 0.517196i | ||||
\(795\) | 0.326575 | − | 0.565644i | 0.0115824 | − | 0.0200613i | ||||
\(796\) | 7.20474 | + | 12.4790i | 0.255365 | + | 0.442306i | ||||
\(797\) | 52.7993 | 1.87025 | 0.935123 | − | 0.354322i | \(-0.115288\pi\) | ||||
0.935123 | + | 0.354322i | \(0.115288\pi\) | |||||||
\(798\) | 0.528521 | + | 5.26504i | 0.0187094 | + | 0.186380i | ||||
\(799\) | −65.4469 | −2.31534 | ||||||||
\(800\) | −0.696708 | − | 1.20673i | −0.0246324 | − | 0.0426645i | ||||
\(801\) | 4.13510 | − | 7.16221i | 0.146107 | − | 0.253064i | ||||
\(802\) | −3.11656 | + | 5.39804i | −0.110050 | + | 0.190611i | ||||
\(803\) | −9.04862 | − | 15.6727i | −0.319319 | − | 0.553076i | ||||
\(804\) | −3.74169 | −0.131959 | ||||||||
\(805\) | −5.43050 | + | 3.90686i | −0.191400 | + | 0.137699i | ||||
\(806\) | −0.786834 | −0.0277150 | ||||||||
\(807\) | −9.81603 | − | 17.0019i | −0.345541 | − | 0.598494i | ||||
\(808\) | −2.69671 | + | 4.67084i | −0.0948699 | + | 0.164319i | ||||
\(809\) | 2.70877 | − | 4.69173i | 0.0952353 | − | 0.164952i | −0.814471 | − | 0.580204i | \(-0.802973\pi\) |
0.909707 | + | 0.415251i | \(0.136306\pi\) | |||||||
\(810\) | −1.26426 | − | 2.18976i | −0.0444216 | − | 0.0769404i | ||||
\(811\) | 42.4931 | 1.49213 | 0.746067 | − | 0.665871i | \(-0.231940\pi\) | ||||
0.746067 | + | 0.665871i | \(0.231940\pi\) | |||||||
\(812\) | 9.89356 | − | 7.11771i | 0.347196 | − | 0.249783i | ||||
\(813\) | −9.37763 | −0.328888 | ||||||||
\(814\) | −19.4518 | − | 33.6915i | −0.681785 | − | 1.18089i | ||||
\(815\) | −15.4928 | + | 26.8343i | −0.542688 | + | 0.939964i | ||||
\(816\) | 3.41196 | − | 5.90969i | 0.119442 | − | 0.206880i | ||||
\(817\) | 2.00000 | + | 3.46410i | 0.0699711 | + | 0.121194i | ||||
\(818\) | 0.369291 | 0.0129120 | ||||||||
\(819\) | 0.103964 | + | 1.03568i | 0.00363281 | + | 0.0361895i | ||||
\(820\) | −7.72979 | −0.269936 | ||||||||
\(821\) | −26.0134 | − | 45.0565i | −0.907874 | − | 1.57248i | −0.817012 | − | 0.576621i | \(-0.804371\pi\) |
−0.0908625 | − | 0.995863i | \(-0.528962\pi\) | |||||||
\(822\) | −8.76440 | + | 15.1804i | −0.305694 | + | 0.529477i | ||||
\(823\) | −20.2016 | + | 34.9901i | −0.704182 | + | 1.21968i | 0.262804 | + | 0.964849i | \(0.415353\pi\) |
−0.966986 | + | 0.254830i | \(0.917981\pi\) | |||||||
\(824\) | 9.07558 | + | 15.7194i | 0.316163 | + | 0.547610i | ||||
\(825\) | −5.98528 | −0.208381 | ||||||||
\(826\) | −24.3948 | − | 10.9981i | −0.848802 | − | 0.382673i | ||||
\(827\) | 1.31040 | 0.0455670 | 0.0227835 | − | 0.999740i | \(-0.492747\pi\) | ||||
0.0227835 | + | 0.999740i | \(0.492747\pi\) | |||||||
\(828\) | 0.500000 | + | 0.866025i | 0.0173762 | + | 0.0300965i | ||||
\(829\) | −10.7042 | + | 18.5402i | −0.371773 | + | 0.643929i | −0.989838 | − | 0.142197i | \(-0.954583\pi\) |
0.618066 | + | 0.786126i | \(0.287917\pi\) | |||||||
\(830\) | 17.2544 | − | 29.8855i | 0.598910 | − | 1.03734i | ||||
\(831\) | −5.96359 | − | 10.3292i | −0.206875 | − | 0.358317i | ||||
\(832\) | 0.393417 | 0.0136393 | ||||||||
\(833\) | −46.8144 | + | 9.49441i | −1.62202 | + | 0.328962i | ||||
\(834\) | −13.0413 | −0.451582 | ||||||||
\(835\) | −6.09342 | − | 10.5541i | −0.210871 | − | 0.365240i | ||||
\(836\) | 4.29540 | − | 7.43985i | 0.148560 | − | 0.257313i | ||||
\(837\) | −1.00000 | + | 1.73205i | −0.0345651 | + | 0.0598684i | ||||
\(838\) | −15.2418 | − | 26.3996i | −0.526520 | − | 0.911960i | ||||
\(839\) | −43.5238 | −1.50261 | −0.751305 | − | 0.659955i | \(-0.770575\pi\) | ||||
−0.751305 | + | 0.659955i | \(0.770575\pi\) | |||||||
\(840\) | 6.09869 | + | 2.74952i | 0.210425 | + | 0.0948676i | ||||
\(841\) | −7.77939 | −0.268255 | ||||||||
\(842\) | −17.1477 | − | 29.7007i | −0.590949 | − | 1.02355i | ||||
\(843\) | −5.33914 | + | 9.24765i | −0.183890 | + | 0.318506i | ||||
\(844\) | −7.59869 | + | 13.1613i | −0.261558 | + | 0.453031i | ||||
\(845\) | 16.2397 | + | 28.1280i | 0.558663 | + | 0.967632i | ||||
\(846\) | −9.59080 | −0.329738 | ||||||||
\(847\) | 1.96886 | + | 19.6135i | 0.0676509 | + | 0.673927i | ||||
\(848\) | 0.258313 | 0.00887051 | ||||||||
\(849\) | −5.61670 | − | 9.72841i | −0.192765 | − | 0.333878i | ||||
\(850\) | −4.75428 | + | 8.23466i | −0.163071 | + | 0.282446i | ||||
\(851\) | 4.52852 | − | 7.84363i | 0.155236 | − | 0.268876i | ||||
\(852\) | −6.93050 | − | 12.0040i | −0.237435 | − | 0.411250i | ||||
\(853\) | 41.2137 | 1.41113 | 0.705566 | − | 0.708645i | \(-0.250693\pi\) | ||||
0.705566 | + | 0.708645i | \(0.250693\pi\) | |||||||
\(854\) | 6.90092 | − | 4.96472i | 0.236145 | − | 0.169889i | ||||
\(855\) | −5.05704 | −0.172947 | ||||||||
\(856\) | −8.29540 | − | 14.3681i | −0.283531 | − | 0.491090i | ||||
\(857\) | −13.7459 | + | 23.8085i | −0.469550 | + | 0.813284i | −0.999394 | − | 0.0348112i | \(-0.988917\pi\) |
0.529844 | + | 0.848095i | \(0.322250\pi\) | |||||||
\(858\) | 0.844941 | − | 1.46348i | 0.0288458 | − | 0.0499624i | ||||
\(859\) | −1.52063 | − | 2.63381i | −0.0518832 | − | 0.0898643i | 0.838917 | − | 0.544259i | \(-0.183189\pi\) |
−0.890801 | + | 0.454394i | \(0.849856\pi\) | |||||||
\(860\) | 5.05704 | 0.172444 | ||||||||
\(861\) | 6.56561 | − | 4.72349i | 0.223755 | − | 0.160976i | ||||
\(862\) | 32.1966 | 1.09662 | ||||||||
\(863\) | −4.85244 | − | 8.40467i | −0.165179 | − | 0.286098i | 0.771540 | − | 0.636181i | \(-0.219487\pi\) |
−0.936719 | + | 0.350083i | \(0.886154\pi\) | |||||||
\(864\) | 0.500000 | − | 0.866025i | 0.0170103 | − | 0.0294628i | ||||
\(865\) | −29.0265 | + | 50.2754i | −0.986932 | + | 1.70942i | ||||
\(866\) | 11.2796 | + | 19.5369i | 0.383297 | + | 0.663890i | ||||
\(867\) | −29.5659 | −1.00411 | ||||||||
\(868\) | −0.528521 | − | 5.26504i | −0.0179392 | − | 0.178707i | ||||
\(869\) | 15.9127 | 0.539803 | ||||||||
\(870\) | 5.82392 | + | 10.0873i | 0.197449 | + | 0.341992i | ||||
\(871\) | −0.736021 | + | 1.27483i | −0.0249391 | + | 0.0431958i | ||||
\(872\) | −7.28280 | + | 12.6142i | −0.246627 | + | 0.427170i | ||||
\(873\) | 4.00000 | + | 6.92820i | 0.135379 | + | 0.234484i | ||||
\(874\) | 2.00000 | 0.0676510 | ||||||||
\(875\) | 21.9954 | + | 9.91639i | 0.743581 | + | 0.335235i | ||||
\(876\) | −4.21317 | −0.142350 | ||||||||
\(877\) | −1.48794 | − | 2.57718i | −0.0502441 | − | 0.0870253i | 0.839810 | − | 0.542881i | \(-0.182667\pi\) |
−0.890054 | + | 0.455856i | \(0.849333\pi\) | |||||||
\(878\) | −2.97481 | + | 5.15252i | −0.100395 | + | 0.173889i | ||||
\(879\) | 11.0882 | − | 19.2053i | 0.373995 | − | 0.647778i | ||||
\(880\) | −5.43050 | − | 9.40591i | −0.183062 | − | 0.317073i | ||||
\(881\) | −26.9064 | −0.906501 | −0.453250 | − | 0.891383i | \(-0.649736\pi\) | ||||
−0.453250 | + | 0.891383i | \(0.649736\pi\) | |||||||
\(882\) | −6.86033 | + | 1.39134i | −0.230999 | + | 0.0468489i | ||||
\(883\) | 19.9159 | 0.670224 | 0.335112 | − | 0.942178i | \(-0.391226\pi\) | ||||
0.335112 | + | 0.942178i | \(0.391226\pi\) | |||||||
\(884\) | −1.34232 | − | 2.32497i | −0.0451472 | − | 0.0781972i | ||||
\(885\) | 12.7868 | − | 22.1474i | 0.429825 | − | 0.744478i | ||||
\(886\) | −7.62197 | + | 13.2016i | −0.256065 | + | 0.443518i | ||||
\(887\) | −8.60393 | − | 14.9024i | −0.288892 | − | 0.500375i | 0.684654 | − | 0.728868i | \(-0.259953\pi\) |
−0.973545 | + | 0.228493i | \(0.926620\pi\) | |||||||
\(888\) | −9.05704 | −0.303934 | ||||||||
\(889\) | −15.1235 | − | 6.81825i | −0.507226 | − | 0.228677i | ||||
\(890\) | −20.9114 | −0.700951 | ||||||||
\(891\) | −2.14770 | − | 3.71993i | −0.0719507 | − | 0.124622i | ||||
\(892\) | 10.5856 | − | 18.3347i | 0.354431 | − | 0.613892i | ||||
\(893\) | −9.59080 | + | 16.6118i | −0.320944 | + | 0.555891i | ||||
\(894\) | −0.0311393 | − | 0.0539349i | −0.00104145 | − | 0.00180385i | ||||
\(895\) | 55.2361 | 1.84634 | ||||||||
\(896\) | 0.264260 | + | 2.63252i | 0.00882832 | + | 0.0879464i | ||||
\(897\) | 0.393417 | 0.0131358 | ||||||||
\(898\) | 11.2744 | + | 19.5278i | 0.376231 | + | 0.651651i | ||||
\(899\) | 4.60658 | − | 7.97884i | 0.153638 | − | 0.266109i | ||||
\(900\) | −0.696708 | + | 1.20673i | −0.0232236 | + | 0.0402245i | ||||
\(901\) | −0.881354 | − | 1.52655i | −0.0293622 | − | 0.0508567i | ||||
\(902\) | −13.1312 | −0.437222 | ||||||||
\(903\) | −4.29540 | + | 3.09023i | −0.142942 | + | 0.102837i | ||||
\(904\) | −9.11932 | −0.303304 | ||||||||
\(905\) | 27.9394 | + | 48.3924i | 0.928735 | + | 1.60862i | ||||
\(906\) | −1.07806 | + | 1.86726i | −0.0358162 | + | 0.0620355i | ||||
\(907\) | 7.96886 | − | 13.8025i | 0.264602 | − | 0.458304i | −0.702858 | − | 0.711331i | \(-0.748093\pi\) |
0.967459 | + | 0.253027i | \(0.0814262\pi\) | |||||||
\(908\) | 1.20474 | + | 2.08667i | 0.0399807 | + | 0.0692487i | ||||
\(909\) | 5.39342 | 0.178888 | ||||||||
\(910\) | 2.13645 | − | 1.53702i | 0.0708227 | − | 0.0509519i | ||||
\(911\) | −30.6965 | −1.01702 | −0.508511 | − | 0.861056i | \(-0.669804\pi\) | ||||
−0.508511 | + | 0.861056i | \(0.669804\pi\) | |||||||
\(912\) | −1.00000 | − | 1.73205i | −0.0331133 | − | 0.0573539i | ||||
\(913\) | 29.3115 | − | 50.7689i | 0.970068 | − | 1.68021i | ||||
\(914\) | −1.05704 | + | 1.83085i | −0.0349638 | + | 0.0605591i | ||||
\(915\) | 4.06228 | + | 7.03607i | 0.134295 | + | 0.232605i | ||||
\(916\) | 10.6160 | 0.350762 | ||||||||
\(917\) | −5.04692 | − | 50.2767i | −0.166664 | − | 1.66028i | ||||
\(918\) | −6.82392 | −0.225223 | ||||||||
\(919\) | −1.33390 | − | 2.31038i | −0.0440012 | − | 0.0762124i | 0.843186 | − | 0.537622i | \(-0.180677\pi\) |
−0.887187 | + | 0.461410i | \(0.847344\pi\) | |||||||
\(920\) | 1.26426 | − | 2.18976i | 0.0416814 | − | 0.0721944i | ||||
\(921\) | −4.00789 | + | 6.94187i | −0.132065 | + | 0.228742i | ||||
\(922\) | −3.00000 | − | 5.19615i | −0.0987997 | − | 0.171126i | ||||
\(923\) | −5.45315 | −0.179493 | ||||||||
\(924\) | 10.3603 | + | 4.67084i | 0.340830 | + | 0.153659i | ||||
\(925\) | 12.6202 | 0.414951 | ||||||||
\(926\) | 1.21317 | + | 2.10127i | 0.0398671 | + | 0.0690519i | ||||
\(927\) | 9.07558 | − | 15.7194i | 0.298081 | − | 0.516292i | ||||
\(928\) | −2.30329 | + | 3.98942i | −0.0756092 | + | 0.130959i | ||||
\(929\) | −23.4770 | − | 40.6634i | −0.770255 | − | 1.33412i | −0.937423 | − | 0.348193i | \(-0.886795\pi\) |
0.167168 | − | 0.985928i | \(-0.446538\pi\) | |||||||
\(930\) | 5.05704 | 0.165827 | ||||||||
\(931\) | −4.45046 | + | 13.2738i | −0.145858 | + | 0.435031i | ||||
\(932\) | 13.1816 | 0.431778 | ||||||||
\(933\) | 10.7954 | + | 18.6982i | 0.353426 | + | 0.612151i | ||||
\(934\) | 9.89356 | − | 17.1361i | 0.323727 | − | 0.560712i | ||||
\(935\) | −37.0573 | + | 64.1852i | −1.21190 | + | 2.09908i | ||||
\(936\) | −0.196708 | − | 0.340709i | −0.00642962 | − | 0.0111364i | ||||
\(937\) | 11.9895 | 0.391681 | 0.195840 | − | 0.980636i | \(-0.437257\pi\) | ||||
0.195840 | + | 0.980636i | \(0.437257\pi\) | |||||||
\(938\) | −9.02480 | − | 4.06873i | −0.294670 | − | 0.132849i | ||||
\(939\) | −13.1816 | −0.430165 | ||||||||
\(940\) | 12.1253 | + | 21.0016i | 0.395483 | + | 0.684996i | ||||
\(941\) | −17.4466 | + | 30.2183i | −0.568742 | + | 0.985090i | 0.427949 | + | 0.903803i | \(0.359236\pi\) |
−0.996691 | + | 0.0812869i | \(0.974097\pi\) | |||||||
\(942\) | 5.54112 | − | 9.59750i | 0.180539 | − | 0.312703i | ||||
\(943\) | −1.52852 | − | 2.64748i | −0.0497755 | − | 0.0862137i | ||||
\(944\) | 10.1141 | 0.329185 | ||||||||
\(945\) | −0.668188 | − | 6.65638i | −0.0217361 | − | 0.216532i | ||||
\(946\) | 8.59080 | 0.279311 | ||||||||
\(947\) | 8.75708 | + | 15.1677i | 0.284567 | + | 0.492884i | 0.972504 | − | 0.232886i | \(-0.0748169\pi\) |
−0.687937 | + | 0.725770i | \(0.741484\pi\) | |||||||
\(948\) | 1.85230 | − | 3.20828i | 0.0601599 | − | 0.104200i | ||||
\(949\) | −0.828765 | + | 1.43546i | −0.0269029 | + | 0.0465971i | ||||
\(950\) | 1.39342 | + | 2.41347i | 0.0452084 | + | 0.0783033i | ||||
\(951\) | 14.2282 | 0.461380 | ||||||||
\(952\) | 14.6557 | − | 10.5438i | 0.474995 | − | 0.341725i | ||||
\(953\) | −13.3209 | −0.431505 | −0.215753 | − | 0.976448i | \(-0.569221\pi\) | ||||
−0.215753 | + | 0.976448i | \(0.569221\pi\) | |||||||
\(954\) | −0.129157 | − | 0.223706i | −0.00418160 | − | 0.00724274i | ||||
\(955\) | 10.4557 | − | 18.1098i | 0.338338 | − | 0.586019i | ||||
\(956\) | −2.12721 | + | 3.68444i | −0.0687989 | + | 0.119163i | ||||
\(957\) | 9.89356 | + | 17.1361i | 0.319813 | + | 0.553933i | ||||
\(958\) | 22.1246 | 0.714812 | ||||||||
\(959\) | −37.6466 | + | 27.0840i | −1.21567 | + | 0.874589i | ||||
\(960\) | −2.52852 | −0.0816077 | ||||||||
\(961\) | 13.5000 | + | 23.3827i | 0.435484 | + | 0.754280i | ||||
\(962\) | −1.78160 | + | 3.08582i | −0.0574410 | + | 0.0994907i | ||||
\(963\) | −8.29540 | + | 14.3681i | −0.267316 | + | 0.463004i | ||||
\(964\) | −7.76688 | − | 13.4526i | −0.250154 | − | 0.433280i | ||||
\(965\) | −16.4543 | −0.529684 | ||||||||
\(966\) | 0.264260 | + | 2.63252i | 0.00850244 | + | 0.0847000i | ||||
\(967\) | −61.9397 | −1.99185 | −0.995923 | − | 0.0902039i | \(-0.971248\pi\) | ||||
−0.995923 | + | 0.0902039i | \(0.971248\pi\) | |||||||
\(968\) | −3.72523 | − | 6.45229i | −0.119733 | − | 0.207384i | ||||
\(969\) | −6.82392 | + | 11.8194i | −0.219216 | + | 0.379693i | ||||
\(970\) | 10.1141 | − | 17.5181i | 0.324744 | − | 0.562472i | ||||
\(971\) | −3.57297 | − | 6.18856i | −0.114662 | − | 0.198600i | 0.802983 | − | 0.596002i | \(-0.203245\pi\) |
−0.917645 | + | 0.397402i | \(0.869912\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −31.4550 | − | 14.1811i | −1.00840 | − | 0.454626i | ||||
\(974\) | 8.54876 | 0.273920 | ||||||||
\(975\) | 0.274097 | + | 0.474750i | 0.00877813 | + | 0.0152042i | ||||
\(976\) | −1.60658 | + | 2.78268i | −0.0514255 | + | 0.0890715i | ||||
\(977\) | 12.1662 | − | 21.0726i | 0.389233 | − | 0.674171i | −0.603114 | − | 0.797655i | \(-0.706074\pi\) |
0.992347 | + | 0.123484i | \(0.0394069\pi\) | |||||||
\(978\) | 6.12721 | + | 10.6126i | 0.195927 | + | 0.339355i | ||||
\(979\) | −35.5238 | −1.13535 | ||||||||
\(980\) | 11.7200 | + | 13.2635i | 0.374380 | + | 0.423687i | ||||
\(981\) | 14.5656 | 0.465044 | ||||||||
\(982\) | −11.2180 | − | 19.4302i | −0.357981 | − | 0.620041i | ||||
\(983\) | 18.0781 | − | 31.3121i | 0.576601 | − | 0.998702i | −0.419265 | − | 0.907864i | \(-0.637712\pi\) |
0.995866 | − | 0.0908377i | \(-0.0289545\pi\) | |||||||
\(984\) | −1.52852 | + | 2.64748i | −0.0487275 | + | 0.0843984i | ||||
\(985\) | −10.3420 | − | 17.9128i | −0.329522 | − | 0.570750i | ||||
\(986\) | 31.4350 | 1.00109 | ||||||||
\(987\) | −23.1326 | − | 10.4291i | −0.736320 | − | 0.331961i | ||||
\(988\) | −0.786834 | −0.0250325 | ||||||||
\(989\) | 1.00000 | + | 1.73205i | 0.0317982 | + | 0.0550760i | ||||
\(990\) | −5.43050 | + | 9.40591i | −0.172593 | + | 0.298939i | ||||
\(991\) | 1.88620 | − | 3.26699i | 0.0599171 | − | 0.103779i | −0.834511 | − | 0.550991i | \(-0.814250\pi\) |
0.894428 | + | 0.447212i | \(0.147583\pi\) | |||||||
\(992\) | 1.00000 | + | 1.73205i | 0.0317500 | + | 0.0549927i | ||||
\(993\) | 21.5975 | 0.685375 | ||||||||
\(994\) | −3.66291 | − | 36.4894i | −0.116181 | − | 1.15737i | ||||
\(995\) | −36.4347 | −1.15506 | ||||||||
\(996\) | −6.82392 | − | 11.8194i | −0.216224 | − | 0.374511i | ||||
\(997\) | 16.6321 | − | 28.8076i | 0.526743 | − | 0.912345i | −0.472772 | − | 0.881185i | \(-0.656747\pi\) |
0.999514 | − | 0.0311600i | \(-0.00992013\pi\) | |||||||
\(998\) | 18.2465 | − | 31.6039i | 0.577584 | − | 1.00040i | ||||
\(999\) | 4.52852 | + | 7.84363i | 0.143276 | + | 0.248161i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 966.2.i.m.277.2 | ✓ | 8 | |
7.2 | even | 3 | inner | 966.2.i.m.415.2 | yes | 8 | |
7.3 | odd | 6 | 6762.2.a.cr.1.2 | 4 | |||
7.4 | even | 3 | 6762.2.a.cl.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
966.2.i.m.277.2 | ✓ | 8 | 1.1 | even | 1 | trivial | |
966.2.i.m.415.2 | yes | 8 | 7.2 | even | 3 | inner | |
6762.2.a.cl.1.3 | 4 | 7.4 | even | 3 | |||
6762.2.a.cr.1.2 | 4 | 7.3 | odd | 6 |